Question

Question 2(iv)
Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:
675

Answer 1

675
Prime factors of $675=3\times 3\times 3\times 5\times 5$
Here factor 5 does not appear in 3’s group.
Therefore 675 must be multiplied by 5 to make it a perfect cube.
$\begin{array}{cc}3& 675\\ 3& 225\\ 3& 75\\ 5& 25\\ 5& 5\\ & 1\end{array}$