Question

Find the cube root of each of the following numbers by prime factorisation method.
(i) $13824$ (ii) $46656$

Answer 1

(i) $13827=2^9\times 3^3$

$\therefore$ $\sqrt[3]{313824}=\sqrt[3]{32^9\times 3^3}=2^3\times 3=24$

(ii) $46656=2^6\times 3^6$

$\therefore$ $\sqrt[3]{346656}=\sqrt[3]{32^6\times 3^6}=2^2\times 3^2=36$