Question

Find the smallest number by which each of the following number must be multiplied to obtain a perfect cube.
(i) $243$ (ii) $256$ (iii) $72$ (iv) $675$ (v) $100$

Answer 1

(i) $243=3^5$

$\therefore 243$ can be made a perfect cube by multiplying it by $3$

(ii) $256=2^8$

$\therefore 256$ can be made a perfect cube by multiplying it by $2$

(iii) $72=3^2\times 2^3$

$\therefore 72$ can be made a perfect cube by multiplying it by $3$

(iv) $675=5^2\times 3^3$

$\therefore 675$ can be made a perfect cube by multiplying it by $5$

(v) $100=2^2\times 5^2$

$\therefore 100$ can be made a perfect cube by multiplying it by $2\times 5=10$