#### Chapters

Chapter 2 - Linear Equations in One Variable

Chapter 3 - Understanding Quadrilaterals

Chapter 4 - Practical Geometry

Chapter 5 - Data Handling

Chapter 6 - Squares and Square Roots

Chapter 7 - Cubes and Cube Roots

Chapter 8 - Comparing Quantities

Chapter 9 - Algebraic Expressions and Identities

Chapter 10 - Visualising Solid Shapes

Chapter 11 - Mensuration

Chapter 12 - Exponents and Powers

Chapter 13 - Direct and Inverse Proportions

Chapter 14 - Factorisation

Chapter 15 - Introduction to Graphs

Chapter 16 - Playing with Numbers

## Chapter 6 - Squares and Square Roots

#### Page 96

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

81

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

55555

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

272

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

799

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

3853

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

1234

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

26387

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

52698

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

99880

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

12796

The following numbers are obviously not perfect squares. Give reason

1057

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

23453

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

7928

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

222222

The following numbers are obviously not perfect squares. Give reason

64000

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

89722

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

222000

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

505050

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

(1) 431

(2) 2826

(3) 7779

(4) 82004

Observe the following pattern and find the missing digits.

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 1…2…1

10000001^{2} = …

Observe the following pattern and supply the missing number.

11^{2} = 121

101^{2} = 10201

10101^{2} = 102030201

1010101^{2} = …

…^{2} = 10203040504030201

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} + _ ^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + _ ^{2} = __^{2}

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

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

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

Express 49 as the sum of 7 odd numbers.

Express 121 as the sum of 11odd numbers.

How many numbers lie between squares of the given numbers?

12 and 13

How many numbers lie between squares of the given numbers?

25 and 26

How many numbers lie between squares of the following numbers?

99 and 100

#### Page 98

Find the square of the given numbers

32

Find the square of the given numbers

35

Find the square of the given numbers

86

Find the square of the given numbers

93

Find the square of the given numbers

71

Find the square of the given numbers

46

Write a Pythagorean triplet whose one member is 6

Write a Pythagorean triplet whose one member is 14

Write a Pythagorean triplet whose one member is 16

Write a Pythagorean triplet whose one member is 18

#### Pages 0 - 103

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

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.

8100

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

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

2028

1458

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

2645

2800

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.

#### Pages 10 - 107

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

2304

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

3136

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

900

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

4489

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

3481

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

529

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

3249

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

1369

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

5776

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

7921

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

576

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

64

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

144

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

4489

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

27225

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

390625

Find the square root of the following decimal number

2.56

Find the square root of the following decimal number

7.29

Find the square root of the following decimal number

51.84

Find the square root of the following decimal number

42.25

Find the square root of the following decimal number

31.36

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

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

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

825

4000

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

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

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

1825

6412

Find the length of the side of a square whose area is 441 m^{2}.

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

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

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.

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?

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

1024