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.
$768$

Answer 1

Given number $=768$

Using prime factorization

$\begin{array}{cc}2& 768\\ 2& 384\\ 2& 192\\ 2& 96\\ 2& 48\\ 2& 24\\ 2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$

$768=(2\times 2)\times (2\times 2)\times (2\times 2)\times (2\times 2)\times 3$

In prime factorization, we have four pairs of $2$ but $3$ has no pair.

So, multiplied by $3$ then it will be perfect square.

$\Rightarrow 768\times 3=2304$

&

$2304=(2\times 2)\times (2\times 2)\times (2\times 2)\times (2\times 2)\times (3\times 3)$

$\sqrt{2304}=2\times 2\times 2\times 2\times 3=48$