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.

180

Answer 1

180 can be factorised as follows:

2	180
2	90
3	45
3	15
5	5
	1

180 = 2 × 2 × 3 × 3 × 5

Here, prime factor 5 does not have its pair. If 5 gets a pair, then the number will become a perfect square. Therefore, 180 has to be multiplied with 5 to obtain a perfect square.

180 × 5 = 900 = 2 × 2 × 3 × 3 × 5 × 5

Therefore, 180 × 5 = 900 is a perfect square.

∴ `sqrt(900)` = 2 × 3 × 5 = 30.