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