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

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Chapter 6 - Squares and Square Roots

Page 96

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

55555

Q 1.1 | Page 96 |

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

81

Q 1.1 | Page 96 |

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

272

Q 1.2 | Page 96 |

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

799

Q 1.3 | Page 96 |

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

3853

Q 1.4 | Page 96 |

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

1234

Q 1.5 | Page 96 |

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

26387

Q 1.6 | Page 96 |

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

52698

Q 1.7 | Page 96 |

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

99880

Q 1.8 | Page 96 |

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

12796

Q 1.9 | Page 96 |

The following numbers are obviously not perfect squares. Give reason

1057

Q 2.1 | Page 96 |

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

23453

Q 2.2 | Page 96 |

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

7928

Q 2.3 | Page 96 |

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

222222

Q 2.4 | Page 96 |

The following numbers are obviously not perfect squares. Give reason

64000

Q 2.5 | Page 96 |

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

89722

Q 2.6 | Page 96 |

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

222000

Q 2.7 | Page 96 |

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

505050

Q 2.8 | Page 96 |

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

(1) 431

(2) 2826

(3) 7779

(4) 82004

Q 3 | Page 96 |

Observe the following pattern and find the missing digits.

112 = 121

1012 = 10201

10012 = 1002001

1000012 = 1…2…1

100000012 = …

Q 4 | Page 96 |

Observe the following pattern and supply the missing number.

112 = 121

1012 = 10201

101012 = 102030201

10101012 = …

2 = 10203040504030201

Q 5 | 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

Q 6 | Page 96 |

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

Q 7.1 | Page 96 |

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

Q 7.2 | Page 96 |

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

Q 7.3 | Page 96 |

Express 49 as the sum of 7 odd numbers.

Q 8.1 | Page 96 |

Express 121 as the sum of 11odd numbers.

Q 8.2 | Page 96 |

How many numbers lie between squares of the given numbers?

12 and 13

Q 9.1 | Page 96 |

How many numbers lie between squares of the given numbers?

25 and 26

Q 9.2 | Page 96 |

How many numbers lie between squares of the following numbers?

99 and 100

Q 9.3 | Page 96 |

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



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.



Pages 10 - 107

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

2304

Q 1.1 | Page 10 |

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

3136

Q 1.11 | Page 107 |

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

900

Q 1.12 | Page 107 |

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

4489

Q 1.2 | Page 107 |

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

3481

Q 1.3 | Page 103 |

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

529

Q 1.4 | Page 107 |

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

3249

Q 1.5 | Page 107 |

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

1369

Q 1.6 | Page 107 |

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

5776

Q 1.7 | Page 107 |

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

7921

Q 1.8 | Page 107 |

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

576

Q 1.9 | Page 107 |

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

64

Q 2.1 | Page 107 |

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

144

Q 2.2 | Page 107 |

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

4489

Q 2.3 | Page 107 |

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

27225

Q 2.4 | Page 107 |

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

390625

Q 2.5 | Page 107 |

Find the square root of the following decimal number

2.56

Q 3.1 | Page 107 |

Find the square root of the following decimal number

7.29

Q 3.2 | Page 107 |

Find the square root of the following decimal number

51.84

Q 3.3 | Page 107 |

Find the square root of the following decimal number

42.25

Q 3.4 | Page 107 |

Find the square root of the following decimal number

31.36

Q 3.5 | Page 107 |

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

Q 4.1 | Page 107 |

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

Q 4.2 | Page 107 |

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

Q 4.3 | Page 107 |

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

Q 4.4 | Page 107 |

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

Q 4.5 | Page 107 |

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

Q 5.1 | Page 107 |

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

Q 5.2 | Page 107 |

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

Q 5.3 | Page 107 |

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

Q 5.4 | Page 107 |

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

Q 5.5 | Page 107 |

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

Q 6 | Page 107 |

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

Q 7.1 | Page 107 |

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

Q 7.2 | Page 107 |

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.

Q 8 | Page 107 |

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?

Q 9 | Page 107 |

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

1024

Q 10 | Page 107 |

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