MCQ
The simplest rationalising factor of $\sqrt[3]{500},$ is:
- A$\sqrt[3]{2}$
- B$\sqrt[3]{5}$
- C$\sqrt{3}$
- DNone of these
✓
Answer
- $\sqrt[3]{2}$
Solution:
$\sqrt[3]{500}=(500)^{\frac{1}{3}}=\Big(\frac{500\times2}{2}\Big)^{\frac{1}{3}}\\ \ =\Big(\frac{1000}{2}\Big)^{\frac{1}{3}}=(10^{\not3})^{\frac{1}{\not3}}.\frac{1}{2^{\frac{1}{3}}}\Rightarrow10.2^{\frac{-1}{3}}$
The simplest Rationalisation factor of $\sqrt[3]{500}$
After simplify it to $\Big(10.2^{\frac{-1}{3}}\Big)$ is $2^{\frac{1}{3}}$ or $\sqrt[3]{2}.$
Hence, correct option is (a).
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