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.

1008

Answer 1

1008 can be factorised as follows:

2	1008
2	504
2	252
2	126
3	63
3	21
7	7
	1

1008 = 2 × 2 × 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, 1008 can be multiplied with 7 to obtain a perfect square.

1008 × 7 = 7056 = 2 × 2 × 2 × 2 × 3 × 3 × 7 × 7

Therefore, 1008 × 7 = 7056 is a perfect square.

∴ `sqrt(7056)` = 2 × 2 × 3 × 7 = 84