# NCERT Solutions for Class 8 Maths

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# Squares and Square Roots

Exercise 1

1.     What will be the unit digit of the squares of the following numbers:

(i) 81            (ii) 272           (iii) 799          (iv) 3853

(v) 1234      (vi) 26387      (vii) 52698     (viii) 99880

(ix) 12796   (x) 55555

2.   The following numbers are obviously not perfect squares. Give reasons.

(i) 1057              (ii) 23453

(iii) 7928           (iv) 222222

(v) 64000          (vi) 89722

(vii) 222000     (viii) 505050

3.   The squares of which of the following would be odd number:

(i) 431             (ii) 2826                (iii) 7779           (iv) 82004

4.   Observe the following pattern and find the missing digits:

112 = 121

1012  = 10201

10012 = 1002001

1000012 = 1….. 2…… 1

10000002 = 1………………….

5.   Observe the following pattern and supply the missing numbers:

112 = 121

1012 = 10201

101012 = 102030201

10101012 = ………………………..

2 = ………… 10203040504030201

6.    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

7.    Without adding, find the sum:

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

8.    (i) Express 49 as the sum of 7 odd numbers.

(ii) Express 121 as the sum of 11 odd numbers.

9.    How many numbers lie between squares of the following numbers:

(i) 12 and 13         (ii) 25 and 26          (iii) 99 and 100.

Exercise 2

10.  Find the squares of the following numbers:

(i) 32

(ii) 35

(iii) 86

(iv) 93

(v) 71

(vi) 46

11.  Write a Pythagoras triplet whose one member is:

(i) 6

(ii) 14

(iii) 16

(iv) 18

Exercise 3

12.  What could be the possible ‘one’s’ digits of the square root of each of the following numbers:

(i)  9801

(ii)  99856

(iii)  998001

(iv)  657666025

13.  Without doing any calculation, find the numbers which are surely not perfect squares:

(i) 153

(ii) 257

(iii) 408

(iv) 441

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

15.  Find the square roots of the following numbers by the Prime Factorization method:

(i) 729             (ii) 400

(iii) 1764         (iv) 4096

(v) 7744          (vi) 9604

(vii) 5929       (viii) 9216

(ix) 529           (x) 8100

16.  For each of the following numbers, 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:

(i) 252          (ii) 180

(iii) 1008     (iv) 2028

(v)  1458       (vi)  768

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

(i) 252           (ii) 2925

(iii) 396        (iv) 2645

(v) 2800      (vi) 1620

18.  The students of Class VIII of a school donated ‘ 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.

19.  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.

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

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

Exercise 4

22.  Find the square roots of each of the following numbers by Division method:

(i) 2304            (ii) 4489

(iii) 3481          (iv) 529

(v) 3249           (vi) 1369

(vii) 5776         (viii) 7921

(ix) 576            (x) 1024

(xi) 3136          (xii) 900

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

(i)  64                (ii) 144

(iii) 4489          (iv) 27225

(v)  390625

24.  Find the square root of the following decimal numbers:

(i) 2.56               (ii) 7.29

(iii) 51.84           (iv) 42.25

(v) 31.36

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

(i) 402                   (ii) 1989

(iii) 3250               (iv) 825

(v) 4000

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

(i) 525                    (ii) 1750

(iii) 252                  (iv) 1825

(v) 6412

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

28.  In a right triangle ABC, ∠ B = 90°.

If AB = 6 cm, BC = 8 cm, find AC.

If AC = 13 cm, BC = 5 cm, find AB.

29.  A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and number of columns remain same. Find the minimum number of plants he needs more for this.

30.  There 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?

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