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Squares And Square Roots

Question
CBSEENMA8002511
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Find the square roots of 100 and 169 by the method of repeated subtraction.

Solution

(i)space space space space space space space space space space space space space space square root of 100
          
      We have      100 - 1 = 99                 99 - 3 = 96            96 - 5 = 91
                        91 - 7 = 84                  84 - 9 = 75            75 - 11 = 64
                        64 - 13 = 51                 51 - 15 = 36           36 - 17 = 19
                         19 - 19 = 0

∵ We reach at 0 by successive subtraction of 10 odd numbers.

∴  space space space space space space space space space space space space space square root of 100 = 10


(1i)space space space space space space space space space space space space space space square root of 169
          
      We have      169 - 1 = 168                 168 - 3 = 165            165 - 5 = 160
                       160 - 7 = 153                 153 - 9 = 144            144 - 11 = 133
                       133 - 13 = 120                120 - 15 = 105          105 - 17 = 88
                         88 - 19 = 69                   69 - 21 = 48             48 - 23 = 25
                         25 - 25 = 0

∵ We reach at 0 by successive subtraction of 13 odd numbers.

∴  space space space space space space space space space space space space space square root of 169 = 13

Some More Questions From Squares and Square Roots Chapter

1. Can we say whether the following numbers are perfect squares? How do we know?

(i) 1057 (ii) 23453 (iii) 7928

(iv) 222222 (v) 1069 (vi) 2061

Write five numbers which you can decide by looking at their one’s digit that they are not square numbers.

Write five numbers which you cannot decide just by looking at their unit’s digit (or one’s place) whether they are square numbers or not.

Which of 1232, 772 822, 1612, 1092 would end with digit 1?

Which of the following numbers would have digit 6 at unit place.

(i) 192 (ii) 242 (iii) 262

(iv) 362 (v) 342

What will be the “one’s digit” in the square of the following numbers?

(i) 1234 (ii) 26387 (iii) 52698

(iv) 99880 (v) 21222 (vi) 9106

The square of which of the following numbers would be an odd number/an even number?

Why?

(i) 727 (ii) 158 (iii) 269 (iv) 1980

What will be the number of zeros in the square of the following numbers?

(i) 60 (ii) 400

How many natural numbers lie between 92 and 102? Between 112 and 122?

How many non-square numbers lie between the following pairs of numbers:
(i) 1002 and 1012 (ii) 902 and 912
(iii) 10002 and 10012

Find whether each of the following numbers is a perfect square or not?

(i) 121 (ii) 55 (iii) 81

(iv) 49 (v) 69

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