Question

Question 5 (vi)

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 number so obtained:

768

Answer 1

$768=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 3$

Here, prime factor 3 has no pair.Therefore

768 must be multiplied by 3 to make it a perfect square.
$\begin{array}{cc}2& 768\\ 2& 384\\ 2& 192\\ 2& 96\\ 2& 48\\ 2& 24\\ 2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$

$\therefore 768\times 3=2304$
And $\sqrt{2304}=2\times 2\times 2\times 2\times 3=48$