A) \[\sqrt[6]{12}\]
B) \[\sqrt[3]{4}\]
C) \[\sqrt{3}\]
D) \[\sqrt[4]{5}\]
Correct Answer: D
Solution :
LCM of indices of surds = LCM of 6, 3, 4 and 2 = 12 \[\therefore \] \[\sqrt[6]{12}=\sqrt[12]{{{12}^{2}}}=\sqrt[12]{144}\] \[\sqrt[3]{4}=\sqrt[12]{{{4}^{4}}}=\sqrt[12]{256}\] \[\sqrt[4]{5}=\sqrt[12]{{{5}^{3}}}=\sqrt[12]{125}\] \[\sqrt{3}=\sqrt[12]{{{3}^{6}}}=\sqrt[12]{729}\] \[\therefore \] The smallest surd \[=\sqrt[4]{5}\]
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