Q.Among \( \sqrt[3]{2}, \sqrt[4]{3}, \sqrt[6]{5} \), the smallest number is — (a) \(\sqrt[3]{2}\) (b) \(\sqrt[4]{3}\) (c) \(\sqrt[6]{5}\) (d) three are same
Answer: A
\((\sqrt[3]{2})^{12} = 2^4 = 16\) \((\sqrt[4]{3})^{12} = 3^3 = 27\) \((\sqrt[6]{5})^{12} = 5^2 = 25\) Here, \( 16 < 25 < 27 \) Therefore, \( \sqrt[3]{2} < \sqrt[6]{5} < \sqrt[4]{3} \) So, the smallest number is \( \sqrt[3]{2} \)
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