Question

The method in which we add first five odd numbers and obtain the square of 5, we subtract odd numbers from 25 and obtain the square root of 25.

Let us see 25 – 1 = 24

24 – 3 = 21
21 – 5 = 16
16 – 7 = 9
9 – 9 = 0

By successive subtraction of first five odd numbers from 25 we get remainder 0. This means square root of 25 is 5. i,e., \(\sqrt{25}\) = 5. You also try to find the square roots of some perfect square numbers using this process.

Answer 1

(i) Let perfect square number is 16 here we subtract the odd numbers 4 time

∴ Square root of 16 = 4

or \(\sqrt{16}\) = 4.

(ii) Let perfect square number is 9. Here we subtract the odd number 3 times.

∴ Square root of 9 = 3 or \(\sqrt{9}\) = 3

(iii) Let a larger number be 36.

Here we have to subtract the odd numbers 6 time.

∴ Square of 36 = 6 or \(\sqrt{36}\) = 6