Question

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

180

Answer 1

$180=2\times 2\times 3\times 3\times 5$

$180=2^2\times 3^2\times 5$
Therefore, factors of 180 are one short of 5 for it to be a complete square. Hence, multiply 180 with 5 to make it a perfect square i.e. 900
Also, $\sqrt{900}=2\times 3\times 5=30$