Question

Qno. 3 Find the square roots of 100 and 169 by the
method of repeated subtraction.​

Answer 1

Answer:

Step-by-step explanation:

We know that the sum of the first 'n' odd natural numbers is n^2. We will use this fact to find square root of a number by repeated subtraction.

1. you are required to find the square root of 100, that is, √100. The steps are:

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

Thus, we have subtracted consecutive odd numbers from 100 starting from 1. 0 is obtained in the 10th step. So we have √100 = 10.

2. you are required to find the square root of 169, that is, √169. The steps are:

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

Thus, we have subtracted consecutive odd numbers from 169 starting from 1. 0 is obtained in the 13th step. So we have √169 = 13.