A) \[\sqrt{2}\]
B) \[\sqrt[3]{3}\]
C) \[\sqrt[4]{4}\]
D) \[\sqrt[6]{6}\]
Correct Answer: B
Solution :
LCM of the orders of the surds = LCM of 2, 3, 4 and 6 = 12 Converting the surds into surds of same order, \[\sqrt{2}=\sqrt[12]{{{2}^{6}}}=\sqrt[12]{64}\] \[\sqrt[3]{3}=\sqrt[12]{{{3}^{4}}}=\sqrt[12]{81}\] \[\sqrt[4]{4}=\sqrt[12]{{{4}^{4}}}=\sqrt[12]{64}\] \[\sqrt[6]{6}=\sqrt[12]{{{6}^{2}}}=\sqrt[12]{36}\] \[\therefore \] The largest number\[=\sqrt[12]{81}=\sqrt[3]{3}\]
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