Question
The simplest rationalisation factor of $\sqrt[3]{500}$ is:
- $\sqrt{5}$
- $\sqrt{3}$
- $\sqrt[3]{5}$
- $\sqrt[3]{2}$
✓
Answer
- $\sqrt[3]{2}$
Solution:
$\sqrt[3]{500}=500^{\frac{1}{3}}=\Big(\frac{500\times2}{2}\Big)^{\frac{1}{3}}$ $=\Big(\frac{1000}{2}\Big)^{\frac{1}{3}}=\frac{10^{3\times\frac{1}{3}}}{2^{\frac{1}{3}}}=\frac{10}{\sqrt[3]{2}}$
Thus, the simplest rationalisation factor of $\sqrt[3]{500}$ is $\sqrt[3]{2}.$
Hence, the correct option is (d).
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