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

Solution:

The sum of the first n odd natural numbers is n2 i.e. every square number can be expressed as a sum of successive odd numbers starting from 1. 

Consider √100

(i) 100 - 1 = 99
(ii) 99 - 3 = 96
(iii) 96 - 5 = 91
(iv) 91 - 7 = 84
(v) 84 - 9 = 75
(vi) 75 - 11 = 64
(vii) 64 - 13 = 51
(viii) 51 - 15 = 36
(ix) 36 - 17 = 19
(x) 19 - 19 = 0

We have subtracted successive odd numbers, and 10 steps have been required for getting the result as 0

So, the square root of 100 is 10

Consider √169

(i) 169 - 1 = 168
(ii) 168 - 3 = 165
(iii) 165 - 5 = 160
(iv) 160 - 7 = 153
(v) 153 - 9 = 144
(vi) 144 - 11 = 133
(vii) 133 - 13 = 120
(viii) 120 - 15 = 105
(ix) 105 - 17 = 88
(x) 88 - 19 = 69
(xi) 69 - 21 = 48
(xii) 48 - 23 = 25
(xiii) 25 - 25 = 0

We have subtracted successive odd numbers, and 13 steps have been required for getting the result as 0

So, the square root of 169 is 13

☛ Check: NCERT Solutions for Class 8 Maths Chapter 6

Video Solution:

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

NCERT Solutions for Class 8 Maths Chapter 6 Exercise 6.3 Question 3

Summary:

The square root of 100 and 169 by using the repeated subtraction method comes out to be 10 and 13.

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