Question : Which is greater $\sqrt[3]{2}$ or $\sqrt{3}$?
Option 1: Cannot be compared.
Option 2: $\sqrt[3]{2}$
Option 3: $\sqrt{3}$
Option 4: Both are equal.
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Correct Answer: $\sqrt{3}$
Solution :
Taking LCM of the given indices i.e., LCM of 2 and 3 is 6.
$\Rightarrow \sqrt[3]{2}=2^\frac{1}{3}=2^\frac{2}{6}=\sqrt[6]{2^2}=\sqrt[6]{4}$
$\Rightarrow \sqrt{3}=3^\frac{1}{2}=3^\frac{3}{6}=\sqrt[6]{3^3}=\sqrt[6]{27}$
Thus, $\sqrt{3}$ is greater.
Hence, the correct answer is $\sqrt{3}$.
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