A) \[\sqrt[3]{4}>\sqrt[4]{5}>\sqrt{2}>\sqrt[6]{3}\]
B) \[\sqrt[4]{5}>\sqrt[3]{4}>\sqrt[6]{3}>\sqrt{2}\]
C) \[\sqrt{2}>\sqrt[6]{3}>\sqrt[3]{4}>\sqrt[4]{5}\]
D) \[\sqrt[6]{3}>\sqrt[4]{5}>\sqrt[3]{4}>\sqrt{2}\]
Correct Answer: A
Solution :
LCM of 3, 2, 6, 4 = 12 \[\because \] \[\sqrt[3]{4}=\sqrt[12]{{{4}^{4}}}=\sqrt[12]{256}\] \[\sqrt{2}=\sqrt[12]{{{2}^{6}}}=\sqrt[12]{64}\] \[\sqrt[6]{3}=\sqrt[12]{{{3}^{2}}}=\sqrt[12]{9}\] \[\sqrt[4]{5}=\sqrt[12]{{{5}^{3}}}=\sqrt[12]{125}\] The decreasing order of the given numbers is \[\sqrt[12]{256}>\sqrt[12]{125}>\sqrt[12]{64}>\sqrt[12]{9}\] \[\Rightarrow \] \[\sqrt[3]{4}>\sqrt[4]{5}>\sqrt{2}>\sqrt[6]{3}\]
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