Which of the following is smallest ?

\sqrt[4]{5}

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\sqrt[5]{4}

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\sqrt{4}

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\sqrt{3}

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Solution

The correct option is C $\sqrt[5]{4}$
Clearly, one of $4^{\frac{1}{5}}$ and $5^{\frac{1}{4}}$ must be the smallest.
$\frac{1}{5}$ < $\frac{1}{4}$ .
So, $4^{\frac{4}{20}}$ < $5^{\frac{5}{20}}$

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