Question

find the number of steps to reduce 169 to 0 by the method of repeated subtraction

Answer 1

Square root by repeated subtraction:

This is the simplest method of finding the square root of a perfect square. It works very well for small numbers.

Take the number n whose square root is required . Subtract from and the odd numbers 1, 3, 5 7, 9….. successively . If n is a perfect square we will get zero at some stage . We stop at this point and declared the number of times we have perform subtraction as the square root of n.


√169 by Repeated subtraction:


1. 169 - 1 = 168
2. 168 - 3 = 165
3. 165 - 5 = 160
4. 160 - 7 = 153
5. 153 - 9 = 144
6. 144 - 11 = 133
7. 133 - 13 = 120
8. 120 - 15 = 105
9. 105 - 17 = 88
10. 88 - 19 = 69
11. 69 - 21 = 48
12. 48 - 23 = 25
13. 25 - 25 = 0


We get 0 at 13th step. Hence,13 is the square root of 169

√169=13