Question

For the following number, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

396

Answer 1

396 can be factorised as follows:

2	396
2	198
3	99
3	33
11	11
	1

396 = 2 × 2 × 3 × 3 × 11

Here, prime factor 11 does not have its pair.

If we divide this number by 11, then the number will become a perfect square. Therefore, 396 has to be divided by 11 to obtain a perfect square.

396 ÷ 11 = 36 is a perfect square.

36 = 2 × 2 × 3 × 3

∴ `sqrt(36)` = 2 × 3 = 6