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

**Solution:**

The sum of the first n odd natural numbers is n^{2} i.e. every square number can be expressed as a sum of successive odd numbers starting from 1.

Consider √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

Consider √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

**Video Solution:**

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

### NCERT Solutions for Class 8 Maths - Chapter 6 Exercise 6.3 Question 3

**Summary:**

The square root of 100 and 169 by using the repeated subtraction method comes out to be 10 and 13.