Find the square root of 169 by the method of repeated subtraction.

The square root of 169 can be obtained by the method of repeated subtraction as follows:

(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 subtracted successive odd numbers starting from 1 to 169 and obtained 0 at the 13^th step.

Therefore, $\sqrt{169}=13$.