NCERT solutions for Mathematics [English] Class 8 chapter 5 - Squares and Square Roots [Latest edition]

What will be the unit digit of the square of the given number?

81

What will be the unit digit of the square of the given number?

272

What will be the unit digit of the square of the given number?

799

What will be the unit digit of the square of the given number?

3853

What will be the unit digit of the square of the given number?

1234

What will be the unit digit of the square of the following number?

26387

What will be the unit digit of the square of the given number?

52698

What will be the unit digit of the square of the following number?

99880

What will be the unit digit of the square of the given number?

12796

What will be the unit digit of the square of the given number?

55555

The following number are obviously not perfect square. Give reason

1057

The following number are obviously not perfect square. Give reason.

23453

The following number are obviously not perfect square. Give reason.

7928

The following number are obviously not perfect square. Give reason.

222222

The following number are obviously not perfect square. Give reason.

64000

The following number are obviously not perfect square. Give reason.

89722

The following number are obviously not perfect square. Give reason.

222000

The following number are obviously not perfect square. 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.

11² = 121

101² = 10201

1001² = 1002001

100001² = 1 ______ 2 ______ 1

10000001² = ______

Observe the following pattern and supply the missing number.

11² = 121

101² = 10201

10101² = 102030201

1010101² = _____

____² = 10203040504030201.

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

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 11 odd 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

Find the square of the given number.

32

Find the square of the given number.

35

Find the square of the given number.

86

Find the square of the given number.

93

Find the square of the given number.

71

Find the square of the given number.

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.

What could be the possible ‘one’s’ digit of the square root of the given number?

9801

What could be the possible ‘one’s’ digit of the square root of the given number?

99856

What could be the possible ‘one’s’ digit of the square root of the given number?

998001

What could be the possible ‘one’s’ digit of the square root of the given number?

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 root of the following number by the prime factorisation method.

729

Find the square root of the following number by the prime factorisation method.

400

Find the square root of the following number by the prime factorisation method.

1764

Find the square root of the following number by the prime factorisation method.

4096

Find the square root of the following number by the prime factorisation method.

7744

Find the square root of the following number by the prime factorisation method.

9604 

Find the square root of the following number by the prime factorisation method.

5929

Find the square root of the following number by the prime factorisation method.

9216

Find the square root of the following number by the prime factorisation method.

529

Find the square root of the following number 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.

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

2304

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 square root of the following number by division method.

1024

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 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 that 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

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

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

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

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

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

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?