Question

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

252 

Answer 1

252 can be factorised as follows:

2	252
2	126
3	63
3	21
7	7
	1

252 = 2 × 2 × 3 × 3 × 7

Here, prime factor 7 does not have its pair.

If 7 gets a pair, then the number will become a perfect square. Therefore, 252 has to be multiplied with 7 to obtain a perfect square.

252 × 7 = 2 × 2 × 3 × 3 × 7 × 7

Therefore, 252 × 7 = 1764 is a perfect square.

∴ `sqrt(1764)` = 2 x 3 x 7 = 42