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.

2028

Answer 1

2028 can be factorised as follows:

2	2028
2	1014
3	507
13	169
13	13
	1

2028 = 2 × 2 × 3 × 13 × 13

Here, prime factor 3 does not have its pair. If 3 gets a pair, then the number will become a perfect square. Therefore, 2028 has to be multiplied with 3 to obtain a perfect square.

Therefore, 2028 × 3 = 6084 is a perfect square.

2028 × 3 = 6084 = 2 × 2 × 3 × 3 × 13 × 13

∴ `sqrt(6084)` = 2 × 3 × 13  = 78