Question

Question 5 (i)
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:

252

Answer 1

$252=2\times 2\times 3\times 3\times 7$

Here, prime factor 7 has no pair. Therefore 252 must be multiplied by 7 to make it a perfect square.

$\therefore 252\times 7=1764$
And $\sqrt{1764}=2\times 3\times 7=42$

$\therefore 252\times 7=1764$
And $\sqrt{1764}=2\times 3\times 7=42\begin{array}{cc}2& 252\\ 2& 126\\ 3& 63\\ 3& 21\\ 7& 7\\ & 1\end{array}$