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 numbers so obtained.
$1008$

Answer 1

Given number $=1008$

Using prime factorization

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

$1008=2\times 2\times 3$

In the above, if ${}^{\prime }{7}^{\prime }$ get a pair then the number will be a perfect square.

$1008\times 7=7056$

& $\sqrt{7056}=2\times 2\times 3\times 7=84$