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# The simplest rationalisation factor of

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).