Among the following, a smallest surd is

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\sqrt{3}

\sqrt[4]{6}

\sqrt[3]{4}

\sqrt{2}

answer is B.

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Detailed Solution

\sqrt[4]{6}

\sqrt{2}

\sqrt[3]{4}

\sqrt{3}

$6^{\frac{1}{4}}, 2^{\frac{1}{2}}, 4^{\frac{1}{3}}, 3^{\frac{1}{2}}$

$L .C .M of 4, 2, 3, 2 is 12$

$6^{\frac{1}{4} \times \frac{3}{3}}, 2^{\frac{1}{2} \times \frac{6}{6}}, 4^{\frac{1}{3} \times \frac{4}{4}}, 3^{\frac{1}{2} \times \frac{6}{6}}$

$6^{\frac{3}{12}}, 2^{\frac{6}{12}}, 4^{\frac{4}{12}}, 3^{\frac{6}{12}}$

$\sqrt[12]{6^{3}}, \sqrt[12]{2^{6}}, \sqrt[12]{4^{4}}, \sqrt[12]{3^{6}}$

$\sqrt[12]{216}, \sqrt[12]{64}, \sqrt[12]{256}, \sqrt[12]{729}$

$\sqrt[12]{64} < \sqrt[12]{216} < \sqrt[12]{256} < \sqrt[12]{729}$

$\sqrt[12]{2^{6}} < \sqrt[12]{6^{3}} < \sqrt[12]{4^{4}} < \sqrt[12]{3^{6}}$

$\sqrt{2} < \sqrt[4]{6} < \sqrt[3]{4} < \sqrt{3}$

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