Book: NCERT - Mathematics
Chapter: 6. Squares and Square Roots
Subject: Maths - Class 8th
Q. No. 3 of Exercises 6.3
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Find the square roots of 100 and 169 by the method of repeated subtraction
The square root of 100 can be obtained by the method of repeated subtraction as:
(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
In this 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:
(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
Hence,
