Question

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

1008

Answer 1

$1008=2\times 2\times 2\times 2\times 3\times 3\times 7$

$1008=2^4\times 3^2\times 7$
Therefore, factors of 1008 are one short of 7 for it to be a complete square. Hence, multiply 1008 with 7 to make it a perfect square i.e. 7056
Also, $\sqrt{7056}=2\times 2\times 3\times 7=84$