Question

Find the smallest number by which 300 must be multiplied so that the product is a perfect square.

Answer 1

Given number is 300 first we resolve it into prime factors

2	300
2	150
3	75
5	25
5	5
	1

$\therefore$ $300=\underset{–}{2\times 2}\times 3\times \underset{–}{5\times 5}$
Clearly 3 has no pair.

Thus, if we multiply it by 3 then the product will be a perfect square.
$\therefore$ Required smallest number is $3$.