Question

Question 5 (ii)

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:

180

Answer 1

$180=2\times 2\times 3\times 3\times 5$

Here, prime factor 5 has no pair. Therefore 180 must be multiplied by 5 to make it a perfect square.

$180=2\times 2\times 3\times 3\times 5\therefore 180\times 5=900$
And $\sqrt{900}=2\times 3\times 5=30\begin{array}{cc}2& 180\\ 2& 90\\ 3& 45\\ 3& 15\\ 5& 5\\ & 1\end{array}$