Which one of the following is least?\( \Large \sqrt{3},\sqrt[3]{2},\sqrt{2},\sqrt[3]{4} \)
Correct Answer: |
B) \( \Large \sqrt[3]{2} \) |
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Description for Correct answer:
\( \Large \sqrt{3},\sqrt[3]{2},\sqrt{2},\sqrt[3]{4} \)
=\( \Large 3^{\frac{1}{2}},2^{\frac{1}{3}},2^{\frac{1}{2}},4^{\frac{1}{3}} \)
(take LCM of 3 and 2)
=\( \Large 3^{\frac{3}{6}},2^{\frac{2}{6}},2^{\frac{3}{6}},4^{\frac{2}{6}} \)
=\( \Large \sqrt[6]{3^{3}},\sqrt[6]{2^{2}},\sqrt[6]{2^{3}},\sqrt[6]{4^{2}} \)
=\( \Large\sqrt[6]{27},\sqrt[6]{4},\sqrt[6]{8},\sqrt[6]{16} \)
=\( \Large \sqrt[3]{2} \)
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