Question

For a given number, find the smallest whole number by which it should be multiplied so as to get a perfect square number.

2028

Answer 1

$2028=2\times 2\times 3\times 13\times 13$

$2028=2^2\times {13}^2\times 3$
2028 is short of one 3 for it to be a perfect square. Hence, it should be multiplied by 3 to get 6084 which is a perfect square.
$\sqrt{6084}=2\times 3\times 13$

$\sqrt{6084}=78$