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

Mathematics Textbook for Class 8

NCERT Mathematics Class 8 Chapter 6: Squares and Square Roots

Ex. 6.10Ex. 6.20Ex. 6.30Ex. 6.40

Chapter 6: Squares and Square Roots Exercise 6.10 solutions [Page 96]

Ex. 6.10 | Q 1.01 | Page 96

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

81

Ex. 6.10 | Q 1.02 | Page 96

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

272

Ex. 6.10 | Q 1.03 | Page 96

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

799

Ex. 6.10 | Q 1.04 | Page 96

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

3853

Ex. 6.10 | Q 1.05 | Page 96

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

1234

Ex. 6.10 | Q 1.06 | Page 96

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

26387

Ex. 6.10 | Q 1.07 | Page 96

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

52698

Ex. 6.10 | Q 1.08 | Page 96

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

99880

Ex. 6.10 | Q 1.09 | Page 96

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

12796

Ex. 6.10 | Q 1.1 | Page 96

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

55555

Ex. 6.10 | Q 2.1 | Page 96

The following numbers are obviously not perfect squares. Give reason

1057

Ex. 6.10 | Q 2.2 | Page 96

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

23453

Ex. 6.10 | Q 2.3 | Page 96

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

7928

Ex. 6.10 | Q 2.4 | Page 96

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

222222

Ex. 6.10 | Q 2.5 | Page 96

The following numbers are obviously not perfect squares. Give reason

64000

Ex. 6.10 | Q 2.6 | Page 96

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

89722

Ex. 6.10 | Q 2.7 | Page 96

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

222000

Ex. 6.10 | Q 2.8 | Page 96

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

505050

Ex. 6.10 | Q 3 | Page 96

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

(1) 431

(2) 2826

(3) 7779

(4) 82004

Ex. 6.10 | Q 4 | Page 96

Observe the following pattern and find the missing digits.

112 = 121

1012 = 10201

10012 = 1002001

1000012 = 1…2…1

100000012 = …

Ex. 6.10 | Q 5 | Page 96

Observe the following pattern and supply the missing number.

112 = 121

1012 = 10201

101012 = 102030201

10101012 = …

2 = 10203040504030201

Ex. 6.10 | 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

Ex. 6.10 | Q 7.1 | Page 96

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

Ex. 6.10 | Q 7.2 | Page 96

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

Ex. 6.10 | Q 7.3 | Page 96

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

Ex. 6.10 | Q 8.1 | Page 96

Express 49 as the sum of 7 odd numbers.

Ex. 6.10 | Q 8.2 | Page 96

Express 121 as the sum of 11odd numbers.

Ex. 6.10 | Q 9.1 | Page 96

How many numbers lie between squares of the given numbers?

12 and 13

Ex. 6.10 | Q 9.2 | Page 96

How many numbers lie between squares of the given numbers?

25 and 26

Ex. 6.10 | Q 9.3 | Page 96

How many numbers lie between squares of the following numbers?

99 and 100

Chapter 6: Squares and Square Roots Exercise 6.20 solutions [Page 98]

Ex. 6.20 | Q 1.1 | Page 98

Find the square of the given numbers

32

Ex. 6.20 | Q 1.2 | Page 98

Find the square of the given numbers

35

Ex. 6.20 | Q 1.3 | Page 98

Find the square of the given numbers

86

Ex. 6.20 | Q 1.4 | Page 98

Find the square of the given numbers

93

Ex. 6.20 | Q 1.5 | Page 98

Find the square of the given numbers

71

Ex. 6.20 | Q 1.6 | Page 98

Find the square of the given numbers

46

Ex. 6.20 | Q 2.1 | Page 98

Write a Pythagorean triplet whose one member is 6

Ex. 6.20 | Q 2.2 | Page 98

Write a Pythagorean triplet whose one member is 14

Ex. 6.20 | Q 2.3 | Page 98

Write a Pythagorean triplet whose one member is 16

Ex. 6.20 | Q 2.4 | Page 98

Write a Pythagorean triplet whose one member is 18

Chapter 6: Squares and Square Roots Exercise 6.30 solutions [Pages 0 - 103]

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

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

99856

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

998001

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

657666025

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

(1) 153

(2) 257

(3) 408

(4) 441

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

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

729

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

400

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

1764

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

4096

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

7744

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

9604

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

5929

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

9216

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

529

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

8100

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

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

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

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

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

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

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

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

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

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

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

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

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.

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.

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

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

Chapter 6: Squares and Square Roots Exercise 6.40 solutions [Pages 10 - 108]

Ex. 6.40 | Q 1.01 | Page 10

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

2304

Ex. 6.40 | Q 1.02 | Page 107

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

4489

Ex. 6.40 | Q 1.03 | Page 103

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

3481

Ex. 6.40 | Q 1.04 | Page 107

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

529

Ex. 6.40 | Q 1.05 | Page 107

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

3249

Ex. 6.40 | Q 1.06 | Page 107

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

1369

Ex. 6.40 | Q 1.07 | Page 107

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

5776

Ex. 6.40 | Q 1.08 | Page 107

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

7921

Ex. 6.40 | Q 1.09 | Page 107

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

576

Ex. 6.40 | Q 1.1 | Page 108

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

1024

Ex. 6.40 | Q 1.11 | Page 107

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

3136

Ex. 6.40 | Q 1.12 | Page 107

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

900

Ex. 6.40 | Q 2.1 | Page 107

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

64

Ex. 6.40 | Q 2.2 | Page 107

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

144

Ex. 6.40 | Q 2.3 | Page 107

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

4489

Ex. 6.40 | Q 2.4 | Page 107

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

27225

Ex. 6.40 | Q 2.5 | Page 107

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

390625

Ex. 6.40 | Q 3.1 | Page 108

Find the square root of the following decimal number

2.56

Ex. 6.40 | Q 3.2 | Page 108

Find the square root of the following decimal number

7.29

Ex. 6.40 | Q 3.3 | Page 108

Find the square root of the following decimal number

51.84

Ex. 6.40 | Q 3.4 | Page 108

Find the square root of the following decimal number

42.25

Ex. 6.40 | Q 3.5 | Page 108

Find the square root of the following decimal number

31.36

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | 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

Ex. 6.40 | Q 6 | Page 108

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

Ex. 6.40 | Q 7.1 | Page 108

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

Ex. 6.40 | Q 7.2 | Page 108

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

Ex. 6.40 | 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.

Ex. 6.40 | 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

Ex. 6.10Ex. 6.20Ex. 6.30Ex. 6.40

NCERT Mathematics Class 8 NCERT solutions for Class 8 Mathematics 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 Mathematics Textbook for Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com are providing 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 Mathematics chapter 6 Squares and Square Roots are Introduction of Square Numbers, Properties of Square Numbers, Some More Interesting Patterns, Finding the Square of a Number - Other Patterns in Squares, Finding the Square of a Number - Pythagorean Triplets, Square Roots - Finding Square Roots, Square Roots - Finding Square Root Through Repeated Subtraction, Square Roots - Finding Square Root Through Prime Factorisation, Square Roots - Finding Square Root by Division Method, Square Roots of Decimals, 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.

Get the free view of chapter 6 Squares and Square Roots Class 8 extra questions for Maths and can use Shaalaa.com to keep it handy for your exam preparation

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