Question

find the square roots of 100 amd 169 by the method of repeated subtraction?​

Answer 1

Step-by-step explanation:

It looks complicated when solve large numbers using this. However, firstly use hit & trial method.

Use those numbers which are used at minimum.

Start with 50:

0 = 100 - 50 - 50 = 100 - (2 x 5) , as 2 & 50 are different. 100 = 50²

There is a big difference in 50 & 2, reduce the next try to 20.

0 = 100 - 20 - 20 - 20 - 20 - 20 = 100 - 5(20), as 5 & 20 are different, 100 ≠ 20²

Now, take 10,

0 = 100 - 10 - 10 - 10 - 10 - 10 - 10 - 10 - 10 - 10 - 10 = 100 - (10 x 10), as both 10 & 10 are same.

100 = 10²

Similarly with 169, at last after performing hit & trial.

0 = 169 - 13 - 13 - 13 - 13 - 13 - 13 - 13 - 13 - 13 - 13 = 169 - (13 x 13) , both 13 & 13 are same.

Hence, 169 = 13²