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We have provided below free printable Class 8 Mathematics Assignments for Download in PDF. The Assignments have been designed based on the latest NCERT Book for Class 8 Mathematics . These Assignments for Grade 8 Mathematics cover all important topics which can come in your standard 8 tests and examinations. Free printable Assignments for CBSE Class 8 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 8 faculty. You can free download CBSE NCERT printable Assignments for Mathematics Class 8 with solutions and answers. All Assignments and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 8. Students can click on the links below and download all Pdf Assignments for Mathematics class 8 for free. All latest Kendriya Vidyalaya Class 8 Mathematics Assignments with Answers and test papers are given below.

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We have provided below the biggest collection of free CBSE NCERT KVS Assignments for Class 8 Mathematics . Students and teachers can download and save all free Mathematics assignments in Pdf for grade 8th. Our expert faculty have covered Class 8 important questions and answers for Mathematics as per the latest syllabus for the current academic year. All test papers and question banks for Class 8 Mathematics and CBSE Assignments for Mathematics Class 8 will be really helpful for standard 8th students to prepare for the class tests and school examinations. Class 8th students can easily free download in Pdf all printable practice worksheets given below.

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Converting Fractions to Decimal

Convert each fraction with a multiple of 10 as its denominator into a decimal number by placing the decimal point at the right spot.

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Finding the Square Roots of Perfect Squares

Apply prime factorization and determine the square roots of the first fifty perfect squares offered as positive integers.

Slope of a Line passing through Two Points

Use the formula, m = (y 2 - y 1 ) / (x 1 - x 1 ) to find the slope(m) of a line passing through two points: (x 1 ,y 1 ) and (x 2 ,y 2 ).

Solving Multi-Step Equations

Follow the order of operations, rearrange to make the unknown variable the subject, and solve for its integer value.

Identifying Functions from Ordered Pairs

Observe each set of ordered pairs given in Part A, figure out ordered pairs from graphs in Part B, and state if they represent a function.

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Find the measure of the indicated interior angle by subtracting the sum of the known angles from 180.

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Observe whether the interior angles lie on the same side or opposite sides of the transversal and find the unknown angle.

Identifying Right Triangles

Square the adjacent and opposite sides of the triangle; take the root of their sum; if you arrive at the hypotenuse, then it's a right triangle.

Volume of Cones

Plug the given radius(r) and height(h) in the formula V = 1/3πr 2 h and find the volume of the cone.

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Read each word problem with a real-life scenario and find the mean, median, mode, and range for each data set.

Converting Fractions to Percent

Switch each fraction to percent by multiplying the numerator by 100, dividing the product by the denominator, and adding the % symbol.

Finding the Square of Square Roots

The square of a square root is the radicand. So, simply multiply the radicand with the square of the number outside the root.

Convert to the Standard Form

Isolate the x and y-terms to one side and the constant to the other side of the equation and rewrite it in the form: ax + by = c.

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Trending Resource : 40+ Activities for the First Week of School

40+ First Week of School Activities

This blog post contains Amazon affiliate links. As an Amazon Associate, I earn a small commission from qualifying purchases.

Looking for ideas as you plan your first day of school math activities? I’ve got enough fun and interactive activities here to last you the entire first week of school and then some!

As summer is wrapping to a close, I am excited to share more than 40 first week of school activities to help you choose the perfect activity for your classroom. The first day of school is one of the highlights of my school year, and I look forward to crafting a fun and engaging experience for my new students each year.

After over a decade in the classroom, I have compiled a list of over forty different tried and tested ideas for the first week of school.

Though I have only taught high school myself, these fun math activities have been tried and tested by thousands of teachers at various grade levels from upper elementary to middle school and high school. 

Each of these lesson ideas features a free download to make it easy to incorporate it into your classroom. As a fellow teacher, I know first-hand just how many things you have on your plate at the beginning of a new school season. 

Getting to Know You Ideas

I always try to include at least one getting to know you idea as a first day of school activity. Here are some various ways that I have done this over the years: 

Getting to Know You Quiz

I like to use a getting to know you quiz to both introduce myself to students and to start learning more about my students. Yes, I am that cruel teacher who gives their students a quiz on the first day of school!

On the front of the quiz, students compete to see who can answer the most questions correctly about their teacher.

After I go over the answers to the quiz about myself, I invite students to write their own quiz about themselves. I take these quizzes after school on the first day of school so that I can return them on the second day of school.

Students love grading my answers and telling me just how well or badly I did!

Want to learn more? Check out my free editable getting to know you quiz template !

When I have had a ton of new names to learn, I really like using  Sara Van Der Werf’s name tents . I have students write their first name on a folded sheet of paper. Inside the paper are various prompts that students respond to on a daily basis which strikes up a conversation between the teacher and the student. 

For the first week of school, I have students get out their name tent at the beginning of the class period. This made it so much easier to learn names!

Getting to Know You Dice Activity

All you will need is a die (I like to use a large foam die ) to pull of this easy-to-implement getting to know you dice activity . Have students take turns rolling a die. Whatever number they roll dictates how many facts about themselves they must share with the class.

You will be sure to hear groans when a student rolls a 6! I always play along as well.

Numbers About Me

A great way to get to know students at the beginning of the school year is to have them fill out a short form like this Numbers About Me Activity . Students write 5 numbers and the significance each number has in their life.

Mathematical Autobiography

I created this mathematical autobiography foldable to try and get an idea of my students’ former experiences with math and attitudes toward math at the beginning of the school year.

Activities for Teaching Group Work

One of the most beneficial ways you can use the first week of school is to teach students how to work effectively in groups. By dedicating the first days of school to teaching group work, you can remind students throughout the year of the lessons learned during the activities. 

Here are some activities I have used to achieve this in the past!

Let’s Make Squares

Let’s Make Squares is a cooperative group work task that challenges students in groups of 4 to use 12 popsicle sticks (or strips of colored paper ) to create various numbers of squares.

Each student is only allowed to touch their own color of popsicle sticks , so they must communicate and practice working together.

They will need to use a bit of logic and creativity to figure out how to make each number of squares.

Broken Circles

In Broken Circles , each student receives an envelope of circle pieces. The goal of the activity is for each student to assemble their pieces to form a complete circle. This activity requires cooperation and communication.

At the beginning of the activity, one student’s pieces will form a circle. The rest of the student’s pieces won’t. It won’t be until the person with the complete circle decides to give some of their pieces to the other students that ALL of the students will be able to make a complete circle.

What an important lesson!

Ink Stain Matching Activity

You might be asking yourself what this ink stain matching activity has to do with teaching math. Fun fact – it absolutely has nothing to do with math. But it has everything to do with practicing critical thinking and communication inside of a group.

Tell your students that 16 items were dipped in ink and then used by an individual. They must work together to match the ink stain left on their hand with the object that they used.

Kids get really into this activity. It’s a definite keeper for the first week of school.

Rainbow Logic

Rainbow Logic is an activity that encourages not only groupwork and communication but logical thinking skills. One student in each group will play the role of “grid designer.” They must arrange colored squares on a 3 x 3 grid using a special set of rules.

The rest of the group must then work together to determine the placement of each of the squares on the grid by asking as few questions as possible.

My students really enjoyed this activity. They didn’t want to stop until everyone had a turn as “Grid Keeper.”

Build It is a cooperative learning activity that provides students with clues and a set of linking cubes that must be assembled to match the clues. The catch?

Each student can only see their own individual clue. This provides great practice in group work communication since each student will need to share their clue verbally and work together to make sure they have created the correct shape with their linking cubes .

With multiple structures to build, this activity is always a great hit!

Survival in the Desert

In Survival in the Desert , groups are given a scenario where their plane has crashed in the desert. They are given a list of items that have been found at the crash site. They must then work together to prioritize the items based on how useful they be for their survival.

The activity encourages communication and creative/logical thinking.

The activity is actually adapted from the Air Force Survival Training Manual. Correct answers are given, and they are always eye-opening to the students!

Guess My Rule

Guess My Rule is a team-building activity that engages students with figuring out the rule that one of their group members is using to sort a set of colored shape cards. Students take turns picking a card to hand to the rule keeper.

The rule keeper will place the card inside the yarn circle if it matches the rule and outside the yarn circle if it does not match the rule. How long will it take students to figure out the rule?

This activity would be great for a geometry class or any math class for that matter! I have used it with Algebra 1 students in the past.

Lonesome Llama

Lonesome Llama is a tricky card-based activity that focuses on encouraging communication, question asking, and attention to detail. Groups are given a deck of cards in which every card has an identical match except one.

Students are only allowed to look at the cards in their own hand. They must then work together to determine which card in the deck has no match. Doesn’t sound too hard, right? Check out the cards!

1-100 Activity

Sara Van Der Werf’s 1-100 Activity is a great way to model groupwork and slowly open students’ eyes to the patterns that exist in mathematics if we are willing to search for them. Students are given a grid of jumbled numbers.

They must take turns coloring the numbers from 1 to 100. Will they notice the pattern???

Master Designer

Master Designer is a group-activity that engages students in building designs and communicating to other students in such a way that their design can be recreated. You will need a set of pattern blocks for each student to use.

Save Fred Activity

In this Save Fred Activity , groups are given a gummy worm named Fred to rescue after his boat has capsized. Students must work together to save Fred without hurting or damaging them.

Each student may only use the provided paperclip to touch the materials as they turn his boat over and retrieve his life preserver that they must place on him.

Puzzles and Brainteasers

If you put me in charge of planning the first week of lessons for a high school math or middle school math classroom, I would make sure to incorporate several different puzzles. You could set these puzzles up as math centers which students rotate through or complete them as a whole-class activity. 

Even though I typed up all of these puzzles for my own high school classroom, I have been absolutely blown away by the number of emails from elementary school teachers I get who are using my puzzles with students as young as 1st grade. So, elementary math teachers could definitely implement some of these puzzles as well. Of course, you will have to pick and choose the puzzles that are most appropriate for your age of students. 

Two Buckets Puzzle

Most likely, you’ve ran across some variation of the two buckets puzzle at some time in your life. You have two buckets. One bucket holds exactly five gallons. The other bucket holds exactly three gallons. How can you measure exactly four gallons of water into the five gallon bucket.

I have used this during the first week of school as a logical thinking activity. Students had to create a poster explaining the process of solving the puzzle to another person.

Petals Around the Rose

Petals Around the Rose is a classic dice-based brain teaser. It can easily be played by the whole class. Roll five dice. Announce how many petals are around the rose. Students must work to figure out the pattern.

The most important element of the game? You aren’t allowed to talk about how the game works! When a student thinks they have solved the mystery, they prove it to the teacher by correctly announcing the number of petals around the rose for several dice throws in a row.

This one is a memorable one, and it tends to drive students CRAZY!

1-4-5 Square Challenge

The 1-4-5 Square Challenge is actually three challenges in one. Can you make a square using exactly 1 piece? How about exactly 4 pieces? Finally, can you make a square using exactly 5 pieces?

Students often struggle with the last challenge and claim it to be impossible until someone in the class finds a solution.

31-derful is a fun, playing card based puzzle. Groups must work together to select 25 cards from a regular deck of playing cards . Then, they must arrange the cards in a 5 x 5 grid so that each row and column sums to 31. Face cards are worth 10. Aces are worth 11.

More Puzzles

I usually do a puzzle of the week with my students in my classroom. I have collected all of the free downloadable puzzles I have created for this challenge on my puzzles page . Any of these puzzles could make a great addition to your first week of school!

Games for the First Week of School

Getting students to play games with one another is one of the best tactics I have in my toolbox for building relationships at the beginning of a new school year. I recommend trying to incorporate at least one game into your lesson plans for the first week of school. 

The Train Game

The Train Game is an absolute favorite in my class. As number tiles are drawn from a bag, students must place the numbers in their “train.” Students earn points for placing the numbers in ascending order.

No erasing or changing numbers is allowed after they have been placed. Students are very competitive when it comes to this game, and they always beg to play just one more round.

Ultimate Tic Tac Toe

All of your students should know how to play tic tac toe. But have they ever experienced ultimate tic tac toe?

In this fun and challenging variation of tic tac toe, each player’s move is influenced by the previous player’s move. This adds a fun level of strategy and challenge!

Students love playing this and Circle Tic Tac Toe below as a tournament!

Circle Tic Tac Toe

Looking for a tic tac toe variation that requires a bit less time? Then, Circle Tic Tac Toe is where it’s at. I got a message from a teacher the other day that his students refused to stop playing!

Instead of getting three in a row, you have to get four in a row. But there is an added twist of having three different ways to win on a circular grid. Print some of these grids off and put them in dry erase pockets in case you have an extra five or ten minutes to spare during the rest of your first week activities.

Thirteen Game

The Thirteen Game is easy to explain to students, and it makes a great time-filling activity for the first week of school. It requires absolutely no supplies or preparation, so it’s a great activity to have in your back pocket.

Students stand in a circle. Choose someone to start. Each player can choose to say either one, two, or three numbers on their turn. Go around the circle counting up from one.

Whoever is forced to say the number thirteen is out. Play continues until only one person remains.

My students get super competitive with this game, and they beg to play it at least once a week for the entire school year. Sometimes they even start up a game by themselves!

My husband tried this game with his middle schoolers, and they absolutely loved it. 

Count to Ten Game

Count to Ten is another great no-prep game that can be played as a moment’s notice. Instruct students that they must count to ten as a class. Talking (other than saying numbers) and hand signals are off-limits.

Only one person may say each number, and no person may say two numbers in a row. If at any time two or more students yell out the same number, the class must start over again at 1.

Students find this activity really hard the first time they do it. It can sometimes take ten or more minutes for a class to get to ten.

Left Center Right Dice Game

If you have a copy of the Left Center Right dice game , it can make a great activity for the first week of school. A former coworker of mine would play the game with starbursts or wrapped candy instead of the plastic discs.

I actually saw that Dollar Tree had copies of Left Center Right in the toy section recently! Usually, I have more students than the discs in the game allows, so I use bingo chips .

My favorite thing about Left Center Right is that even if you’re out of the game, you can still end up winning! It’s also great for discussing statistics and probability .

Sprouts is a mathematical game that is easy to teach students. It only requires something to write with and something to write on. I love using dry erase boards to teach students how to play Sprouts in pairs.

The basic idea of the game is to make it impossible for your opponent to draw a line. The last person to draw a line is the winner.

There are more rules, of course. You can read about them here. A Sprouts Tournament can be a fun addition to the first week of school after you teach students to play Sprouts in pairs.

Make A Million Game

In Make a Million , a ten-sided die is rolled twelve times. After each roll, students must place the number rolled in their make a million template. When finished, students sum the two numbers they have created to see how close they got to a million. I usually give a piece of candy to the student who gets the closest.

Usually, the first time we play this, my students place the numbers almost randomly. After seeing how things play out, it is exciting to see how their strategies start to change!  

Traffic Lights Game

The Traffic Lights Game is easy to teach but hard to master. You will need printable game boards and traffic light colored bingo chips . Students compete to get three-in-a-row of a single color. On any turn, you may place a red chip on an empty square, switch a red chip to a yellow chip, or switch a yellow chip to a green chip.

Such a great strategy game! I have often modeled how to play on the SMARTBoard with my students before I leave them to play on their own.

Witzzle is a card/ dice game that gives so many opportunities for practicing mental math and the order of operations in the math classroom. I like to create a Witzzle Bulletin Board in my classroom and introduce students to the game during the first week of school.

Once students know the rules, I can easily use it as an early-finisher activity or brain break throughout the rest of the school year.

How do you play Witzzle? A target number is announced by the teacher. Students must find a row, column, or diagonal of numbers that can be used to make the target. Numbers can be added, subtracted, multiplied, or divided in any order.

The cards in a witzzle game are specially designed so that every number from -12 to 36 can be achieved.

The Game of SET

Another favorite mathematical game that I often like to introduce students to at the beginning of the year is the game of SET . SET is a card game that can be played alone or with a group that relies on pattern recognition.

If you don’t have a deck of SET cards, you can play it with students using the Daily SET Puzzle .

I have had some students become super obsessed with the SET game! One year, I had a student beg to take a deck home over the weekend so she could play with her mom. I find that if I teach students how to play SET during the first week of school that it makes a great warm-up or time-filler activity throughout the rest of the school year.    

Here are several other games that would make a great addition to your first week of school (or any time throughout the school year!)

• Martinetti Dice Game
• Slam Dice Game
• Greedy Pig Dice Game
• The Game of 24
• Sara Van Der Werf’s 5 x 5 Game
• Skittles Game
• Cover Up Game
• Numerical Tic Tac Toe
• Wild Tic Tac Toe

Engineering and Building Challenges for the First Week of School

Cup stacking challenge.

This cup stacking challenge uses everyday materials (string, cups, and a rubber band for each group) and really encourages students to communicate and work together to build each structure.

Each student can only touch their individual string which is tied to the group’s rubber band which is used to move the cups in the challenge. Be prepared for a room full of laughter as students experiment!

Marshmallow Challenge

In the Marshmallow Challenge , small groups compete to see who can build the tallest tower using a limited amount of dried spaghetti, tape, and string. The completed tower must be free-standing and support a marshmallow at the top of the tower.

Impossible Domino Bridge

If you have some wooden dominoes laying around, you have all you need for this Impossible Domino Bridge building activity .

Spoiler alert: it’s not actually impossible. But it might seem that way to students.

This is a great way to teach perseverance in problem solving during the first week of school.

Impossible Domino Tower

Then, you can use those same dominoes to have your students tackle the impossible domino tower challenge .

Mathematical Tasks for the First Week of School

Twos to nines challenges.

One of my favorite first day activities ever would have to be the Twos to Nines Challenges . Students work in small groups to create the given numbers using exactly four of a given number. I set up different challenges for each number around the room.

On top of being fun, this is a great way of getting students thinking about math, doing mental math, and reviewing the order of operations. This is a nice extension of the usual Four Fours task.

Prefer printable paper based versions of these same challenges? I have slowly been turning them into printable activities that are perfect for sliding inside a dry erase pocket !

• Twos Challenge
• Threes Challenge
• Fours Challenge
• Fives Challenge
• Sixes Challenge
• Sevens Challenge

Five Easy Pieces

Five Easy Pieces combines paper folding, algebra, and logic puzzles into one great activity that is a perfect review activity for the beginning of the school year. Students have to follow a set of instructions to create a set of paper pieces that are then used to answer a series of math problems.

A Mathematical Magic Trick

I used this mathematical magic trick with students during my first year of teaching. The magic trick starts with students thinking of a number from 1 to 10, and it ends with almost every student thinking of the exact same animal in the exact same country eating the exact same food.

Is it magic? Or is it math?

Digit Cells

Digit Cells is an interesting math puzzle that asks students to write a 10 digit number so that the digit in the first cell tells how many zeros are in the entire 10 digit number. The digit in the cell marked “1” tells how many “1’s” are in the number, and so on.

Students always think this puzzle must be impossible at first, so it’s always a joy to watch their faces when they finally solve it.

Twelve Envelopes Puzzle

I have used the twelve envelopes puzzle with students during the first week before. It’s a fun math puzzle that provides a great review of divisibility rules!

Divisibility Puzzle

Another quick puzzle to review divisibility rules is this fun divisibility puzzle which involves placing the digits 0-9 in the blanks to create 10 true statements about divisibility rules.

More Math Challenges

• Make Six Number Challenge
• 9-10-11-12 Challenge
• 97 Free Tangram Challenges

20 x 9 Challenge

• Yearly Number Challenge
• The 5-4-3-2-1 Challenge
• 3-1-4 Pi Challenge

More Fun Activities for the First Week of School

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

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54 comments.

Hi Sarah, So appreciative of all of your hard work and energy. Was wondering if you could send the build-it cards? I've purchased the blocks through your affiliate link and would love to get to use them with this activity. sweetesbakere[at]gmail.com

These are all awesome. I don't think I'll have time to try all of them but I'm certainly going to try a couple. In your Make a Million activity, is it okay if they go over? Are you just looking for who is closest even if it's bigger than 1 million?

And I love SET! I've never tried it in a classroom before but I might. How many do you usually have in a group for that?

I also really want to try the get to know you activity. How long did you spend on each of these activities?

The idea of Lonesome Llama is awesome. i really appreciate the idea with all your hard work & efforts.

Sarah, thank you so much for all of the free resources! I could not find your Build It cards, though. Am I overlooking them? If you wouldn't mind, could you send them to me at jrobrown7[at]gmail.com? I would greatly appreciate it!

These activities are great. What grades would you suggest for these activities?

Great activities! Thank you for sharing. I am looking forward to trying a few of these with my students this coming year.

Awesome! I really like all of them! (I totally love SET). I understood you have 15-16 year students? I guess I will adapt some of them for 12 to 14. Thank you very much for your generosity! By the way, do you know The GAME? I really really recommend it.

Sarah, This Blog is amazing, I can't wait to share all your activities with the teachers I work with. I couldn't find a link to the "Build It" cards from the photos. I was wondering if you could email me a copy of the cards you use. [email protected]

Thanks again for all the resources you have shared!

I am having trouble downloading these great activites. Would you be able to send me another link? I teach special education and these look great.

I love your Getting to Know You quiz and was wondering if you have a template for the multiple choice questions paper that you have the students fill out?

I have shared the template for the Getting to Know You Quiz Here: https://mathequalslove.net/getting-to-know-you-quiz/

Sarah, you are such an amazing and talented teacher who is the most generous person, too. It is so awesome you’ve tried these out and have given your activities for back to school which is sure to be challenging. Thank you. Blessings and good fortune to you and Sean, and your family

Thank you so much Pat!

Thanks so much for all the great ideas!

Here is one I use… Students make a timeline of their lives 10 facts about themselves starting with their bday and ending with the first day of school this year below the timeline and 10 world history events within their lives above the timeline

I use this in both math and social studies classes It’s shocking how many students don’t know how to properly space a timeline I do an example so they get to know me and then their timeline gives me info about each student

Have a great year! I’m still only 2/3 through summer school!

I like this idea! Thanks for sharing!

This is a fabulous list! My fifth grade classes started this week and we have enjoyed both Broken Circles and Build It. We got a little stuck on Build It #3. I told my class I would email you to ask if there is an answer key somewhere to check. If not, thank you anyway for this list!

Someone else reported that there were two conflicting cards. They said that after they removed one of the cards that it worked perfectly. Sorry I can’t tell you which card to remove. To my knowledge, there is not an answer key.

After reading Peter Liljedahl’s Building Thinking Classrooms Book, I’m wondering how these activities might be modified for groups of 3. Have you done any of those that currently need 4 folks with groups of 3 instead?

I think that Let’s Make Squares could easily be adapted to 3. Just use 3 colors of popsicle sticks instead of 4. Broken Circles has a 3 person version, but it is DRASTICALLY easier than the 4 person version.

Rainbow Logic, Build It, Master Designer and Guess My Rule would all work just fine with groups of 3. I have seen a 3 person version of the 100 Numbers activity floating around on facebook. They arranged the numbers in a circle.

Almost all of them could be adapted for groups of 3, I think!

If anyone else has adapted an activity for groups of 3, leave a comment!

Comments are closed.

• NCERT Solutions
• NCERT Class 8
• NCERT 8 Maths
• Chapter 6: Square Square Roots

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots

Ncert solutions class 8 maths chapter 6 – free pdf download.

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots are beneficial for students since it aids them in scoring high marks in the exam. The subject experts at BYJU’S outline the concepts in a distinct and well-defined manner, keeping the IQ level of students in mind. These solution modules use various shortcut hints and practical examples to explain all the exercise questions in simple and easily understandable language. Solving the NCERT Class 8 Solutions is a must to obtain an excellent score in the examination.

Download Exclusively Curated Chapter Notes for Class 8 Maths Chapter – 6 Squares and Square Roots

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Here, with the NCERT Solutions provided, the students will learn various techniques to determine whether a given natural number is a perfect square or not. The answers to all problems within this chapter present in NCERT Textbooks are provided here in a detailed and step-by-step way to help the students understand more effectively. Students can download the NCERT Solutions for Class 8 Maths Chapter 6 from the link provided below.

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Exercise 6.1 Page: 96

1. What will be the unit digit of the squares of the following numbers?

viii. 99880

The unit digit of square of a number having ‘a’ at its unit place ends with a×a.

i. The unit digit of the square of a number having digit 1 as unit’s place is 1.

∴ Unit digit of the square of number 81 is equal to 1.

ii. The unit digit of the square of a number having digit 2 as unit’s place is 4.

∴ Unit digit of the square of number 272 is equal to 4.

iii. The unit digit of the square of a number having digit 9 as unit’s place is 1.

∴ Unit digit of the square of number 799 is equal to 1.

iv. The unit digit of the square of a number having digit 3 as unit’s place is 9.

∴ Unit digit of the square of number 3853 is equal to 9.

v. The unit digit of the square of a number having digit 4 as unit’s place is 6.

∴ Unit digit of the square of number 1234 is equal to 6.

vi. The unit digit of the square of a number having digit 7 as unit’s place is 9.

∴ Unit digit of the square of number 26387 is equal to 9.

vii. The unit digit of the square of a number having digit 8 as unit’s place is 4.

∴ Unit digit of the square of number 52698 is equal to 4.

viii. The unit digit of the square of a number having digit 0 as unit’s place is 01.

∴ Unit digit of the square of number 99880 is equal to 0.

ix. The unit digit of the square of a number having digit 6 as unit’s place is 6.

∴ Unit digit of the square of number 12796 is equal to 6.

x. The unit digit of the square of a number having digit 5 as unit’s place is 5.

∴ Unit digit of the square of number 55555 is equal to 5.

2. The following numbers are obviously not perfect squares. Give reason.

vii. 222000

viii. 505050

We know that natural numbers ending in the digits 0, 2, 3, 7 and 8 are not perfect squares.

i. 1057 ⟹ Ends with 7

ii. 23453 ⟹ Ends with 3

iii. 7928 ⟹ Ends with 8

iv. 222222 ⟹ Ends with 2

v. 64000 ⟹ Ends with 0

vi. 89722 ⟹ Ends with 2

vii. 222000 ⟹ Ends with 0

viii. 505050 ⟹ Ends with 0

3. The squares of which of the following would be odd numbers?

We know that the square of an odd number is odd and the square of an even number is even.

i. The square of 431 is an odd number.

ii. The square of 2826 is an even number.

iii. The square of 7779 is an odd number.

iv. The square of 82004 is an even number.

4. Observe the following pattern and find the missing numbers. 11 2 = 121

101 2 = 10201

1001 2 = 1002001

100001 2 = 1 …….2………1

10000001 2 = ……………………..

We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1 and middle digit is 2. And the number of zeros between left most digits 1 and the middle digit 2 and right most digit 1 and the middle digit 2 is same as the number of zeros in the given number.

∴ 100001 2 = 10000200001

10000001 2 = 100000020000001

5. Observe the following pattern and supply the missing numbers. 112 = 121

1012 = 10201

101012 = 102030201

10101012 = ………………………

…………2 = 10203040504030201

We observe that the square on the number on R.H.S of the equality has an odd number of digits such that the first and last digits both are 1. And, the square is symmetric about the middle digit. If the middle digit is 4, then the number to be squared is 10101 and its square is 102030201.

So, 10101012 =1020304030201

1010101012 =10203040505030201

6. Using the given pattern, find the missing numbers. 1 2 + 2 2 + 2 2 = 3 2

2 2 + 3 2 + 6 2 = 7 2

3 2 + 4 2 + 12 2 = 13 2

4 2 + 5 2 + _2 = 21 2

5 + _ 2 + 30 2 = 31 2

6 + 7 + _ 2 = _ 2

Given, 1 2 + 2 2 + 2 2 = 3 2

i.e 1 2 + 2 2 + (1×2 ) 2 = ( 1 2 + 2 2 -1 × 2 ) 2

2 2 + 3 2 + 6 2 =7 2

∴ 2 2 + 3 2 + (2×3 ) 2 = (2 2 + 3 2 -2 × 3) 2

∴ 3 2 + 4 2 + (3×4 ) 2 = (3 2 + 4 2 – 3 × 4) 2

4 2 + 5 2 + (4×5 ) 2 = (4 2 + 5 2 – 4 × 5) 2

∴ 4 2 + 5 2 + 20 2 = 21 2

5 2 + 6 2 + (5×6 ) 2 = (5 2 + 6 2 – 5 × 6) 2

∴ 5 2 + 6 2 + 30 2 = 31 2

6 2 + 7 2 + (6×7 ) 2 = (6 2 + 7 2 – 6 × 7) 2

∴ 6 2 + 7 2 + 42 2 = 43 2

7. Without adding, find the sum.

i. 1 + 3 + 5 + 7 + 9

Sum of first five odd number = (5) 2 = 25

ii. 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19

Sum of first ten odd number = (10) 2 = 100

iii. 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Sum of first thirteen odd number = (12) 2 = 144

8. (i) Express 49 as the sum of 7 odd numbers.

We know, sum of first n odd natural numbers is n 2 . Since,49 = 7 2

∴ 49 = sum of first 7 odd natural numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13

(ii) Express 121 as the sum of 11 odd numbers.

Since, 121 = 11 2

∴ 121 = sum of first 11 odd natural numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

9. How many numbers lie between squares of the following numbers?

i. 12 and 13

ii. 25 and 26

iii. 99 and 100

Between n 2 and (n+1) 2 , there are 2n non–perfect square numbers.

i. 122 and 132 there are 2×12 = 24 natural numbers.

ii. 252 and 262 there are 2×25 = 50 natural numbers.

iii. 992 and 1002 there are 2×99 =198 natural numbers.

Exercise 6.2 Page: 98

1. Find the square of the following numbers.

= (30 +2) 2

= 900 + 4 + 120

= (30+5 ) 2

= 900 + 25 + 300

iii. (86) 2

= (90 – 4) 2

= 8100 + 16 – 720

= 8116 – 720

= (90+3 ) 2

= 8100 + 9 + 540

= (70+1 ) 2

= 4900 + 1 + 140

= (50 -4 ) 2

= 2500 + 16 – 400

2. Write a Pythagorean triplet whose one member is.

For any natural number m, we know that 2m, m2–1, m2+1 is a Pythagorean triplet.

⇒ m = 6/2 = 3

m2–1= 32 – 1 = 9–1 = 8

m2+1= 32+1 = 9+1 = 10

∴ (6, 8, 10) is a Pythagorean triplet.

ii. 2m = 14

⇒ m = 14/2 = 7

m2–1= 72–1 = 49–1 = 48

m2+1 = 72+1 = 49+1 = 50

∴ (14, 48, 50) is not a Pythagorean triplet.

iii. 2m = 16

⇒ m = 16/2 = 8

m2–1 = 82–1 = 64–1 = 63

m2+ 1 = 82+1 = 64+1 = 65

∴ (16, 63, 65) is a Pythagorean triplet.

iv. 2m = 18

⇒ m = 18/2 = 9

m2–1 = 92–1 = 81–1 = 80

m2+1 = 92+1 = 81+1 = 82

∴ (18, 80, 82) is a Pythagorean triplet.

Exercise 6.3 Page: 102

1. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?

iii. 998001

iv. 657666025

i. We know that the unit’s digit of the square of a number having digit as unit’s

place 1 is 1 and also 9 is 1[9 2 =81 whose unit place is 1].

∴ Unit’s digit of the square root of number 9801 is equal to 1 or 9.

ii. We know that the unit’s digit of the square of a number having digit as unit’s

place 6 is 6 and also 4 is 6 [6 2 =36 and 4 2 =16, both the squares have unit digit 6].

∴ Unit’s digit of the square root of number 99856 is equal to 6.

iii. We know that the unit’s digit of the square of a number having digit as unit’s

∴ Unit’s digit of the square root of number 998001 is equal to 1 or 9.

iv. We know that the unit’s digit of the square of a number having digit as unit’s

place 5 is 5.

∴ Unit’s digit of the square root of number 657666025 is equal to 5.

2. Without doing any calculation, find the numbers which are surely not perfect squares.

We know that natural numbers ending with the digits 0, 2, 3, 7 and 8 are not perfect square.

i. 153⟹ Ends with 3.

∴, 153 is not a perfect square

ii. 257⟹ Ends with 7

∴, 257 is not a perfect square

iii. 408⟹ Ends with 8

∴, 408 is not a perfect square

iv. 441⟹ Ends with 1

∴, 441 is a perfect square.

3. Find the square roots of 100 and 169 by the method of repeated subtraction .

100 – 1 = 99

99 – 3 = 96

96 – 5 = 91

91 – 7 = 84

84 – 9 = 75

75 – 11 = 64

64 – 13 = 51

51 – 15 = 36

36 – 17 = 19

19 – 19 = 0

Here, we have performed subtraction ten times.

∴ √100 = 10

169 – 1 = 168

168 – 3 = 165

165 – 5 = 160

160 – 7 = 153

153 – 9 = 144

144 – 11 = 133

133 – 13 = 120

120 – 15 = 105

105 – 17 = 88

88 – 19 = 69

69 – 21 = 48

48 – 23 = 25

25 – 25 = 0

Here, we have performed subtraction thirteen times.

∴ √169 = 13

4. Find the square roots of the following numbers by the Prime Factorisation Method.

729 = 3×3×3×3×3×3×1

⇒ 729 = (3×3)×(3×3)×(3×3)

⇒ 729 = (3×3×3)×(3×3×3)

⇒ 729 = (3×3×3) 2

⇒ √729 = 3×3×3 = 27

400 = 2×2×2×2×5×5×1

⇒ 400 = (2×2)×(2×2)×(5×5)

⇒ 400 = (2×2×5)×(2×2×5)

⇒ 400 = (2×2×5) 2

⇒ √400 = 2×2×5 = 20

1764 = 2×2×3×3×7×7

⇒ 1764 = (2×2)×(3×3)×(7×7)

⇒ 1764 = (2×3×7)×(2×3×7)

⇒ 1764 = (2×3×7) 2

⇒ √1764 = 2 ×3×7 = 42

4096 = 2×2×2×2×2×2×2×2×2×2×2×2

⇒ 4096 = (2×2)×(2×2)×(2×2)×(2×2)×(2×2)×(2×2)

⇒ 4096 = (2×2×2×2×2×2)×(2×2×2×2×2×2)

⇒ 4096 = (2×2×2×2×2×2) 2

⇒ √4096 = 2×2×2 ×2×2×2 = 64

7744 = 2×2×2×2×2×2×11×11×1

⇒ 7744 = (2×2)×(2×2)×(2×2)×(11×11)

⇒ 7744 = (2×2×2×11)×(2×2×2×11)

⇒ 7744 = (2×2×2×11) 2

⇒ √7744 = 2×2×2×11 = 88

9604 = 62 × 2 × 7 × 7 × 7 × 7

⇒ 9604 = ( 2 × 2 ) × ( 7 × 7 ) × ( 7 × 7 )

⇒ 9604 = ( 2 × 7 ×7 ) × ( 2 × 7 ×7 )

⇒ 9604 = ( 2×7×7 ) 2

⇒ √9604 = 2×7×7 = 98

5929 = 7×7×11×11

⇒ 5929 = (7×7)×(11×11)

⇒ 5929 = (7×11)×(7×11)

⇒ 5929 = (7×11) 2

⇒ √5929 = 7×11 = 77

9216 = 2×2×2×2×2×2×2×2×2×2×3×3×1

⇒ 9216 = (2×2)×(2×2) × ( 2 × 2 ) × ( 2 × 2 ) × ( 2 × 2 ) × ( 3 × 3 )

⇒ 9216 = ( 2 × 2 × 2 × 2 × 2 × 3) × ( 2 × 2 × 2 × 2 × 2 × 3)

⇒ 9216 = 96 × 96

⇒ 9216 = ( 96 ) 2

⇒ √9216 = 96

529 = 23×23

529 = (23) 2

8100 = 2×2×3×3×3×3×5×5×1

⇒ 8100 = (2×2) ×(3×3)×(3×3)×(5×5)

⇒ 8100 = (2×3×3×5)×(2×3×3×5)

⇒ 8100 = 90×90

⇒ 8100 = (90) 2

⇒ √8100 = 90

5. For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained.

252 = 2×2×3×3×7

= (2×2)×(3×3)×7

Here, 7 cannot be paired.

∴ We will multiply 252 by 7 to get perfect square.

New number = 252 × 7 = 1764

⇒ 1764 = 2 2 ×3 2 ×7 2

⇒ √1764 = 2×3×7 = 42

180 = 2×2×3×3×5

= (2×2)×(3×3)×5

Here, 5 cannot be paired.

∴ We will multiply 180 by 5 to get perfect square.

New number = 180 × 5 = 900

900 = 2×2×3×3×5×5×1

⇒ 900 = (2×2)×(3×3)×(5×5)

⇒ 900 = 2 2 ×3 2 ×5 2

⇒ 900 = (2×3×5) 2

⇒ √900 = 2×3×5 = 30

1008 = 2×2×2×2×3×3×7

= (2×2)×(2×2)×(3×3)×7

∴ We will multiply 1008 by 7 to get perfect square.

New number = 1008×7 = 7056

7056 = 2×2×2×2×3×3×7×7

⇒ 7056 = (2×2)×(2×2)×(3×3)×(7×7)

⇒ 7056 = 2 2 ×2 2 ×3 2 ×7 2

⇒ 7056 = (2×2×3×7) 2

⇒ √7056 = 2×2×3×7 = 84

2028 = 2×2×3×13×13

= (2×2)×(13×13)×3

Here, 3 cannot be paired.

∴ We will multiply 2028 by 3 to get perfect square. New number = 2028×3 = 6084

6084 = 2×2×3×3×13×13

⇒ 6084 = (2×2)×(3×3)×(13×13)

⇒ 6084 = 2 2 ×3 2 ×13 2

⇒ 6084 = (2×3×13) 2

⇒ √6084 = 2×3×13 = 78

1458 = 2×3×3×3×3×3×3

= (3×3)×(3×3)×(3×3)×2

Here, 2 cannot be paired.

∴ We will multiply 1458 by 2 to get perfect square. New number = 1458 × 2 = 2916

2916 = 2×2×3×3×3×3×3×3

⇒ 2916 = (3×3)×(3×3)×(3×3)×(2×2)

⇒ 2916 = 3 2 ×3 2 ×3 2 ×2 2

⇒ 2916 = (3×3×3×2) 2

⇒ √2916 = 3×3×3×2 = 54

768 = 2×2×2×2×2×2×2×2×3

= (2×2)×(2×2)×(2×2)×(2×2)×3

∴ We will multiply 768 by 3 to get perfect square.

New number = 768×3 = 2304

2304 = 2×2×2×2×2×2×2×2×3×3

⇒ 2304 = (2×2)×(2×2)×(2×2)×(2×2)×(3×3)

⇒ 2304 = 2 2 ×2 2 ×2 2 ×2 2 ×3 2

⇒ 2304 = (2×2×2×2×3) 2

⇒ √2304 = 2×2×2×2×3 = 48

6. For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained.

∴ We will divide 252 by 7 to get perfect square. New number = 252 ÷ 7 = 36

36 = 2×2×3×3

⇒ 36 = (2×2)×(3×3)

⇒ 36 = 2 2 ×3 2

⇒ 36 = (2×3) 2

⇒ √36 = 2×3 = 6

2925 = 3×3×5×5×13

= (3×3)×(5×5)×13

Here, 13 cannot be paired.

∴ We will divide 2925 by 13 to get perfect square. New number = 2925 ÷ 13 = 225

225 = 3×3×5×5

⇒ 225 = (3×3)×(5×5)

⇒ 225 = 3 2 ×5 2

⇒ 225 = (3×5) 2

⇒ √36 = 3×5 = 15

396 = 2×2×3×3×11

= (2×2)×(3×3)×11

Here, 11 cannot be paired.

∴ We will divide 396 by 11 to get perfect square. New number = 396 ÷ 11 = 36

2645 = 5×23×23

⇒ 2645 = (23×23)×5

∴ We will divide 2645 by 5 to get perfect square.

New number = 2645 ÷ 5 = 529

⇒ 529 = (23) 2

⇒ √529 = 23

2800 = 2×2×2×2×5×5×7

= (2×2)×(2×2)×(5×5)×7

∴ We will divide 2800 by 7 to get perfect square. New number = 2800 ÷ 7 = 400

400 = 2×2×2×2×5×5

⇒ √400 = 20

1620 = 2×2×3×3×3×3×5

= (2×2)×(3×3)×(3×3)×5

∴ We will divide 1620 by 5 to get perfect square. New number = 1620 ÷ 5 = 324

324 = 2×2×3×3×3×3

⇒ 324 = (2×2)×(3×3)×(3×3)

⇒ 324 = (2×3×3) 2

⇒ √324 = 18

7. The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Let the number of students in the school be, x.

∴ Each student donate Rs.x .

Total amount contributed by all the students= x×x=x 2 Given, x 2 = Rs.2401

x 2 = 7×7×7×7

⇒ x 2 = (7×7)×(7×7)

⇒ x 2 = 49×49

⇒ x = √(49×49)

∴ The number of students = 49

8. 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

Let the number of rows be, x.

∴ the number of plants in each rows = x.

Total plants to be planted in the garden = x × x =x 2

x 2 = Rs.2025

x 2 = 3×3×3×3×5×5

⇒ x 2 = (3×3)×(3×3)×(5×5)

⇒ x2 = (3×3×5)×(3×3×5)

⇒ x2 = 45×45

⇒ x = √45×45

∴ The number of rows = 45 and the number of plants in each rows = 45.

9. Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

L.C.M of 4, 9 and 10 is (2×2×9×5) 180.

180 = 2×2×9×5

= (2×2)×3×3×5

∴ we will multiply 180 by 5 to get perfect square.

Hence, the smallest square number divisible by 4, 9 and 10 = 180×5 = 900

10. Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

L.C.M of 8, 15 and 20 is (2×2×5×2×3) 120.

120 = 2×2×3×5×2

= (2×2)×3×5×2

Here, 3, 5 and 2 cannot be paired.

∴ We will multiply 120 by (3×5×2) 30 to get perfect square.

Hence, the smallest square number divisible by 8, 15 and 20 =120×30 = 3600

Exercise 6.4 Page: 107

1. Find the square root of each of the following numbers by Division method.

∴ √2304 = 48

∴ √4489 = 67

∴ √3481 = 59

∴ √529 = 23

∴ √3249 = 57

∴ √1369 = 37

∴ √5776 = 76

∴ √7921 = 89

∴ √576 = 24

∴ √1024 = 32

∴ √3136 = 56

∴ √900 = 30

2. Find the number of digits in the square root of each of the following numbers (without any

calculation).64

∴ √144 = 12

Hence, the square root of the number 144 has 2 digits.

Hence, the square root of the number 4489 has 2 digits.

√27225 = 165

Hence, the square root of the number 27225 has 3 digits.

∴ √390625 = 625

Hence, the square root of the number 390625 has 3 digits.

3. Find the square root of the following decimal numbers.

∴ √2.56 = 1.6

∴ √7.29 = 2.7

∴ √51.84 = 7.2

∴ √42.25 = 6.5

∴ √31.36 = 5.6

4. Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

∴ We must subtract 2 from 402 to get a perfect square.

New number = 402 – 2 = 400

∴ √400 = 20

∴ We must subtract 53 from 1989 to get a perfect square. New number = 1989 – 53 = 1936

∴ √1936 = 44

∴ We must subtract 1 from 3250 to get a perfect square.

New number = 3250 – 1 = 3249

∴ We must subtract 41 from 825 to get a perfect square.

New number = 825 – 41 = 784

∴ √784 = 28

∴ We must subtract 31 from 4000 to get a perfect square. New number = 4000 – 31 = 3969

∴ √3969 = 63

5. Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

Here, (22)2 < 525 > (23)2

We can say 525 is ( 129 – 125 ) 4 less than (23)2.

∴ If we add 4 to 525, it will be perfect square. New number = 525 + 4 = 529

Here, (41)2 < 1750 > (42) 2

We can say 1750 is ( 164 – 150 ) 14 less than (42) 2 .

∴ If we add 14 to 1750, it will be perfect square.

New number = 1750 + 14 = 1764

∴√1764 = 42

Here, (15)2 < 252 > (16)2

We can say 252 is ( 156 – 152 ) 4 less than (16)2.

∴ If we add 4 to 252, it will be perfect square.

New number = 252 + 4 = 256

∴ √256 = 16

Here, (42)2 < 1825 > (43)2

We can say 1825 is ( 249 – 225 ) 24 less than (43)2.

∴ If we add 24 to 1825, it will be perfect square.

New number = 1825 + 24 = 1849

∴ √1849 = 43

Here, (80)2 < 6412 > (81)2

We can say 6412 is ( 161 – 12 ) 149 less than (81)2.

∴ If we add 149 to 6412, it will be perfect square.

New number = 6412 + 149 = 656

∴ √6561 = 81

6. Find the length of the side of a square whose area is 441 m2.

Let the length of each side of the field = a Then, area of the field = 441 m2

⇒ a2 = 441 m2

⇒a = √441 m

∴ The length of each side of the field = a m = 21 m.

7. In a right triangle ABC, ∠B = 90°.

a. If AB = 6 cm, BC = 8 cm, find AC

b. If AC = 13 cm, BC = 5 cm, find AB

Given, AB = 6 cm, BC = 8 cm

Let AC be x cm.

∴ AC2 = AB2 + BC2

Hence, AC = 10 cm.

Given, AC = 13 cm, BC = 5 cm

Let AB be x cm.

⇒ AC2 – BC2 = AB2

Hence, AB = 12 cm

8. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows

and the number of columns remain same. Find the minimum number of plants he needs more for this.

Let the number of rows and column be, x.

∴ Total number of row and column= x× x = x2 As per question, x2 = 1000

⇒ x = √1000

Here, (31)2 < 1000 > (32)2

We can say 1000 is ( 124 – 100 ) 24 less than (32)2.

∴ 24 more plants are needed.

9. There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.

∴ Total number of row and column= x × x = x2 As per question, x2 = 500

Hence, 16 children would be left out in the arrangement

NCERT Solutions for Class 8 Maths Chapter 6 – Squares and Square Roots

The NCERT Solutions for Class 8 Maths Chapter 8 deals with the concept of squares and square roots, along with other main topics and concepts.

The major concepts covered in this chapter include:

6.1 Introduction

6.2 Properties of Square Numbers

6.3 Some interesting patterns

6.4 Finding the square of a number

6.4.1 Patterns in Squares

6.4.2 Pythagorean triplets

6.5 Square Roots

6.5.1 Finding square roots

6.5.2 Finding square root through repeated subtraction

6.5.3 Finding square root through prime factorisation

6.5.4 Finding square Root by division method

6.6 Square Roots of Decimals

6.7 Estimating Square Root

Below are the exercise-wise NCERT Solutions for Class 8 Maths Chapter 6:

Exercise 6.1 Solutions 9 Questions

Exercise 6.2 Solutions 2 Questions

Exercise 6.3 Solutions 10 Questions

Exercise 6.4 Solutions 9 Questions

NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots – Summary

Chapter 6 of NCERT Solutions for Class 8 Maths discusses the following:

• If a natural number m can be expressed as n 2 , where n is a natural number, then m is a square number.
• All square numbers end with 0, 1, 4, 5, 6 or 9 at units place.
• Square numbers can only have an even number of zeros at the end.
• Square root is the inverse operation of square.
• There are two integral square roots of a perfect square number

Learning the chapter Squares and Square Roots enables the students to understand:

• Square and Square roots
• Square roots using the factor method and division method for numbers containing(a) no more than a total of 4 digits and (b) no more than 2 decimal places
• Estimating square roots
• Learning the process of moving nearer to the required number

Disclaimer:

Dropped Topics – 6.7 Estimating square roots.

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