Question

Find the smallest no. by which of the following no. must be multiplied to obtain a perfect cube.
(i) $243$
(ii) $256$
(iii) $72$
(iv) $675$
(v) $100$

Answer 1

(i) $243=3\times 3\times 3\times 3\times 3=$ $3^3\times 3\times 3$
Required no $=3$
(ii) $256=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2=$ $2^3\times 2^3\times 2\times 2$
Required no. $=2$
(iii) $72=2\times 2\times 2\times 3\times 3=$ $2^3\times 3\times 3$
Required no. $=3$
(iv) $675=5\times 5\times 3\times 3\times 3=$ $3^3\times 5\times 5$
Required no. $=5$
(v) $100=2\times 2\times 5\times 5$
Required no. $=2\times 5=10$