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Asked by Sumathi Last Modified
Answer We know that the sum of the first n odd natural numbers is n2.
Consider
.
(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 starting from 1 to 100, and obtained 0 at 10th step.
Therefore, 
The square root of 169 can be obtained by the method of repeated subtraction as follows.
(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 starting from 1 to 169, and obtained 0 at 13th step.
Therefore,
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