Question

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

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Answer 1

$\mathsf{Consider \: \red{\sqrt{ 100}}}$

• (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.

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$\mathsf{Consider \: \red{ \sqrt{169}}}$

• (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.

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Answer 2

Answer:

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Step-by-step explanation:

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