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