# NCERT solutions for Class 8 Maths chapter 6 - Squares and Square Roots [Latest edition]

## Chapter 6: Squares and Square Roots

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4
Exercise 6.1 [Page 96]

### NCERT solutions for Class 8 Maths Chapter 6 Squares and Square RootsExercise 6.1 [Page 96]

Exercise 6.1 | Q 1.01 | Page 96

What will be the unit digit of the squares of the given numbers?

81

Exercise 6.1 | Q 1.02 | Page 96

What will be the unit digit of the squares of the given numbers?

272

Exercise 6.1 | Q 1.03 | Page 96

What will be the unit digit of the squares of the given numbers?

799

Exercise 6.1 | Q 1.04 | Page 96

What will be the unit digit of the squares of the given numbers?

3853

Exercise 6.1 | Q 1.05 | Page 96

What will be the unit digit of the squares of the given numbers?

1234

Exercise 6.1 | Q 1.06 | Page 96

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

26387

Exercise 6.1 | Q 1.07 | Page 96

What will be the unit digit of the squares of the given numbers?

52698

Exercise 6.1 | Q 1.08 | Page 96

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

99880

Exercise 6.1 | Q 1.09 | Page 96

What will be the unit digit of the squares of the given numbers?

12796

Exercise 6.1 | Q 1.1 | Page 96

What will be the unit digit of the squares of the given numbers?

55555

Exercise 6.1 | Q 2.1 | Page 96

The following numbers are obviously not perfect squares. Give reason

1057

Exercise 6.1 | Q 2.2 | Page 96

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

23453

Exercise 6.1 | Q 2.3 | Page 96

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

7928

Exercise 6.1 | Q 2.4 | Page 96

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

222222

Exercise 6.1 | Q 2.5 | Page 96

The following numbers are obviously not perfect squares. Give reason

64000

Exercise 6.1 | Q 2.6 | Page 96

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

89722

Exercise 6.1 | Q 2.7 | Page 96

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

222000

Exercise 6.1 | Q 2.8 | Page 96

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

505050

Exercise 6.1 | Q 3 | Page 96

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

(1) 431

(2) 2826

(3) 7779

(4) 82004

Exercise 6.1 | Q 4 | Page 96

Observe the following pattern and find the missing digits.

112 = 121

1012 = 10201

10012 = 1002001

1000012 = 1…2…1

100000012 = …

Exercise 6.1 | Q 5 | Page 96

Observe the following pattern and supply the missing number.

112 = 121

1012 = 10201

101012 = 102030201

10101012 = …

2 = 10203040504030201

Exercise 6.1 | Q 6 | Page 96

Using the given pattern, find the missing numbers.

12 + 22 + 22 = 32

22 + 32 + 62 = 72

32 + 42 + 122 = 132

42 + 52 + _ 2 = 212

52 + _ 2 + 302 = 312

62 + 72 + _ 2 = __2

Exercise 6.1 | Q 7.1 | Page 96

Without adding find the sum 1 + 3 + 5 + 7 + 9

Exercise 6.1 | Q 7.2 | Page 96

Without adding find the sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

Exercise 6.1 | Q 7.3 | Page 96

Without adding find the sum 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

Exercise 6.1 | Q 8.1 | Page 96

Express 49 as the sum of 7 odd numbers.

Exercise 6.1 | Q 8.2 | Page 96

Express 121 as the sum of 11odd numbers.

Exercise 6.1 | Q 9.1 | Page 96

How many numbers lie between squares of the given numbers?

12 and 13

Exercise 6.1 | Q 9.2 | Page 96

How many numbers lie between squares of the given numbers?

25 and 26

Exercise 6.1 | Q 9.3 | Page 96

How many numbers lie between squares of the following numbers?

99 and 100

Exercise 6.2 [Page 98]

### NCERT solutions for Class 8 Maths Chapter 6 Squares and Square RootsExercise 6.2 [Page 98]

Exercise 6.2 | Q 1.1 | Page 98

Find the square of the given numbers

32

Exercise 6.2 | Q 1.2 | Page 98

Find the square of the given numbers

35

Exercise 6.2 | Q 1.3 | Page 98

Find the square of the given numbers

86

Exercise 6.2 | Q 1.4 | Page 98

Find the square of the given numbers

93

Exercise 6.2 | Q 1.5 | Page 98

Find the square of the given numbers

71

Exercise 6.2 | Q 1.6 | Page 98

Find the square of the given numbers

46

Exercise 6.2 | Q 2.1 | Page 98

Write a Pythagorean triplet whose one member is 6

Exercise 6.2 | Q 2.2 | Page 98

Write a Pythagorean triplet whose one member is 14

Exercise 6.2 | Q 2.3 | Page 98

Write a Pythagorean triplet whose one member is 16

Exercise 6.2 | Q 2.4 | Page 98

Write a Pythagorean triplet whose one member is 18

Exercise 6.3 [Pages 102 - 103]

### NCERT solutions for Class 8 Maths Chapter 6 Squares and Square RootsExercise 6.3 [Pages 102 - 103]

Exercise 6.3 | Q 1.1 | Page 102

What could be the possible ‘one’s’ digits of the square root of the given numbers?
9801

Exercise 6.3 | Q 1.2 | Page 102

What could be the possible ‘one’s’ digits of the square root of the given numbers?

99856

Exercise 6.3 | Q 1.3 | Page 102

What could be the possible ‘one’s’ digits of the square root of the given numbers?

998001

Exercise 6.3 | Q 1.4 | Page 102

What could be the possible ‘one’s’ digits of the square root of the given numbers?

657666025

Exercise 6.3 | Q 2 | Page 102

Without doing any calculation, find the number which are surely not perfect squares

(1) 153

(2) 257

(3) 408

(4) 441

Exercise 6.3 | Q 3 | Page 102

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

Exercise 6.3 | Q 4.01 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

729

Exercise 6.3 | Q 4.02 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

400

Exercise 6.3 | Q 4.03 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

1764

Exercise 6.3 | Q 4.04 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

4096

Exercise 6.3 | Q 4.05 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

7744

Exercise 6.3 | Q 4.06

Find the square roots of the given numbers by the Prime Factorisation Method.

9604

Exercise 6.3 | Q 4.07 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

5929

Exercise 6.3 | Q 4.08 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

9216

Exercise 6.3 | Q 4.09 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

529

Exercise 6.3 | Q 4.1 | Page 102

Find the square roots of the given numbers by the Prime Factorisation Method.

8100

Exercise 6.3 | Q 5.1 | Page 102

For the following number, 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

Exercise 6.3 | Q 5.2 | Page 102

For the following number, 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.

180

Exercise 6.3 | Q 5.3 | Page 102

For the following number, 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.

1008

Exercise 6.3 | Q 5.4 | Page 102

For the following number, 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.

2028

Exercise 6.3 | Q 5.5 | Page 102

For the following number, 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.

1458

Exercise 6.3 | Q 5.6 | Page 102

For the following number, 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.

768

Exercise 6.3 | Q 6.1 | Page 102

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

252

Exercise 6.3 | Q 6.2 | Page 102

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

2925

Exercise 6.3 | Q 6.3 | Page 102

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

396

Exercise 6.3 | Q 6.4 | Page 102

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

2645

Exercise 6.3 | Q 6.5 | Page 102

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

2800

Exercise 6.3 | Q 6.6 | Page 102

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

1620

Exercise 6.3 | Q 7 | Page 102

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.

Exercise 6.3 | Q 8 | Page 103

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.

Exercise 6.3 | Q 9 | Page 103

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

Exercise 6.3 | Q 10 | Page 103

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

Exercise 6.4 [Pages 10 - 108]

### NCERT solutions for Class 8 Maths Chapter 6 Squares and Square RootsExercise 6.4 [Pages 10 - 108]

Exercise 6.4 | Q 1.01 | Page 10

Find the square root of the following number by division method.

2304

Exercise 6.4 | Q 1.02 | Page 107

Find the square root of the following number by division method.

4489

Exercise 6.4 | Q 1.03 | Page 103

Find the square root of the following number by division method.

3481

Exercise 6.4 | Q 1.04 | Page 107

Find the square root of the following number by division method.

529

Exercise 6.4 | Q 1.05 | Page 107

Find the square root of the following number by division method.

3249

Exercise 6.4 | Q 1.06 | Page 107

Find the square root of the following number by division method.

1369

Exercise 6.4 | Q 1.07 | Page 107

Find the square root of the following number by division method.

5776

Exercise 6.4 | Q 1.08 | Page 107

Find the square root of the following number by division method.

7921

Exercise 6.4 | Q 1.09 | Page 107

Find the square root of the following number by division method.

576

Exercise 6.4 | Q 1.1 | Page 108

Find the square root of the following number by division method.

1024

Exercise 6.4 | Q 1.11 | Page 107

Find the square root of the following number by division method.

3136

Exercise 6.4 | Q 1.12 | Page 107

Find the square root of the following number by division method.

900

Exercise 6.4 | Q 2.1 | Page 107

Find the number of digits in the square root of the following numbers (without any calculation).

64

Exercise 6.4 | Q 2.2 | Page 107

Find the number of digits in the square root of the following numbers (without any calculation).

144

Exercise 6.4 | Q 2.3 | Page 107

Find the number of digits in the square root of the following numbers (without any calculation).

4489

Exercise 6.4 | Q 2.4 | Page 107

Find the number of digits in the square root of the following numbers (without any calculation).

27225

Exercise 6.4 | Q 2.5 | Page 107

Find the number of digits in the square root of the following numbers (without any calculation).

390625

Exercise 6.4 | Q 3.1 | Page 108

Find the square root of the following decimal number

2.56

Exercise 6.4 | Q 3.2 | Page 108

Find the square root of the following decimal number

7.29

Exercise 6.4 | Q 3.3 | Page 108

Find the square root of the following decimal number

51.84

Exercise 6.4 | Q 3.4 | Page 108

Find the square root of the following decimal number

42.25

Exercise 6.4 | Q 3.5 | Page 108

Find the square root of the following decimal number

31.36

Exercise 6.4 | Q 4.1 | Page 108

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

402

Exercise 6.4 | Q 4.2 | Page 108

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

1989

Exercise 6.4 | Q 4.3 | Page 108

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

3250

Exercise 6.4 | Q 4.4 | Page 108

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

825

Exercise 6.4 | Q 4.5 | Page 108

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

4000

Exercise 6.4 | Q 5.1 | Page 108

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

525

Exercise 6.4 | Q 5.2 | Page 108

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

1750

Exercise 6.4 | Q 5.3 | Page 108

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

252

Exercise 6.4 | Q 5.4 | Page 108

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

1825

Exercise 6.4 | Q 5.5 | Page 108

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

6412

Exercise 6.4 | Q 6 | Page 108

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

Exercise 6.4 | Q 7.1 | Page 108

In a right triangle ABC, ∠B = 90° If AB = 6 cm, BC = 8 cm, find AC

Exercise 6.4 | Q 7.2 | Page 108

In a right triangle ABC, ∠B = 90°. If AC = 13 cm, BC = 5 cm, find AB

Exercise 6.4 | Q 8 | Page 108

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.

Exercise 6.4 | Q 9 | Page 108

These 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?

## Chapter 6: Squares and Square Roots

Exercise 6.1Exercise 6.2Exercise 6.3Exercise 6.4

## NCERT solutions for Class 8 Maths chapter 6 - Squares and Square Roots

NCERT solutions for Class 8 Maths chapter 6 (Squares and Square Roots) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 6 Squares and Square Roots are Properties of Square Numbers, Some More Interesting Patterns of Square Number, Square Root of Decimal Numbers, Concept of Square Number, Finding the Square of a Number, Concept of Square Roots, Finding Square Root Through Repeated Subtraction, Finding Square Root Through Prime Factorisation, Finding Square Root by Division Method, Estimating Square Root.

Using NCERT Class 8 solutions Squares and Square Roots exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

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