Question

Find the square roots of 121 and 169 by the method of repeated subtraction.

Answer 1

To find the square root of 121:
121 − 1 = 120
120 − 3 = 117
117 − 5 = 112
112 − 7 = 105
105 − 9 = 96
96 − 11 = 85
85 − 13 = 72
72 − 15 = 57
57 − 17 = 40
40 − 19 = 21
21 − 21 = 0
In total, there are 11 numbers to subtract from 121. Hence, the square root of 121 is 11.

To find the square root of 169:
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
In total, there are 13 numbers to subtract from 169. Hence, the square root of 169 is 13.