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.

1458

Answer 1

1458 can be factorised as follows:

2	1458
3	729
3	243
3	81
3	27
3	9
3	3
	1

1458 = 2 × 3 × 3 × 3 × 3 × 3 × 3

Here, prime factor 2 does not have its pair. If 2 gets a pair, then the number will become a perfect square. Therefore, 1458 has to be multiplied with 2 to obtain a perfect square.

Therefore, 1458 × 2 = 2916 is a perfect square.

1458 × 2 = 2916 = 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

∴ `sqrt(2916)` = 2 × 3 × 3 × 3 = 54