Question

Question 5 (iii)

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:

1008

Answer 1

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

$\begin{array}{cc}2& 1008\\ 2& 504\\ 2& 252\\ 2& 126\\ 3& 63\\ 3& 21\\ 7& 7\\ & 1\end{array}$

Here, prime factor 7 has no pair. Therefore 1008 must be multiplied by 7 to make it a perfect square.

$\therefore 1008\times 7=7056$
And $\sqrt{7056}=2\times 2\times 3\times 7=84$