Which is the greatest number among sqrt[3]{9} | vedclass

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(A) To compare the numbers $\sqrt[3]{9}, \sqrt[4]{11}, \sqrt[6]{17}$,we convert them to the same root index.The least common multiple $(L.C.M.)$ of th

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$\sqrt[3]{9}$

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(A) To compare the numbers $\sqrt[3]{9}, \sqrt[4]{11}, \sqrt[6]{17}$,we convert them to the same root index.The least common multiple $(L.C.M.)$ of the indices $3, 4, 6$ is $12$.$\sqrt[3]{9} = 9^{1/3} = (9^4)^{1/12} = (6561)^{1/12}$$\sqrt[4]{11} = 11^{1/4} = (11^3)^{1/12} = (1331)^{1/12}$$\sqrt[6]{17} = 17^{1/6} = (17^2)^{1/12} = (289)^{1/12}$Comparing the values inside the brackets: $6561 > 1331 > 289$.Therefore,$\sqrt[3]{9}$ is the greatest number.

Which is the greatest number among $\sqrt[3]{9}, \sqrt[4]{11}, \sqrt[6]{17}$?

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