Question

The simplest rationalisation factor of $\sqrt[3]{500}$ is
(a) $\sqrt{5}$
(b) $\sqrt{3}$
(c) $\sqrt[3]{5}$
(d) $\sqrt[3]{2}$

Answer 1

$\sqrt[3]{500}=\sqrt[3]{5\times 5\times 2\times 5\times 2}=\sqrt[3]{5^3\times 2^2}=5\sqrt[3]{4}$
So, the simplest rationalisation factor of $\sqrt[3]{500}$ is $\sqrt[3]{2}$.
Hence, the correct answer is option (d).