A) \[\sqrt[3]{4}\]
B) \[\sqrt{2}\]
C) \[\sqrt[6]{3}\]
D) \[\sqrt[4]{5}\]
Correct Answer: A
Solution :
\[\sqrt[3]{4},\sqrt{2},\sqrt[6]{3},\sqrt[4]{5}\] LCM of 3, 2, 6, 4 = 12 \[\sqrt[3]{4}={{(4)}^{1/3}}={{(4)}^{4/12}}={{({{4}^{4}})}^{1/12}}={{(256)}^{1/12}}\] \[\sqrt{2}={{(2)}^{1/2}}={{(2)}^{6/12}}={{({{2}^{6}})}^{1/12}}={{(64)}^{1/12}}\] \[\sqrt[6]{3}={{(3)}^{1/6}}={{(3)}^{2/12}}={{({{3}^{2}})}^{1/12}}={{(9)}^{1/12}}\] \[\sqrt[4]{5}={{(5)}^{1/4}}={{(5)}^{3/12}}={{({{5}^{3}})}^{1/12}}={{(125)}^{1/12}}\] \[\therefore \] \[\sqrt[3]{4}>\sqrt[4]{5}>\sqrt{2}>\sqrt[6]{3}\]
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