Question

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

• A. $\sqrt[3]{9}$
• B. $\sqrt[4]{11}$
• C. $\sqrt[6]{17}$
• D. Can not be determined

Answer 1

Answer: (A)

$\sqrt[3]{9}$

Answer 2

$\sqrt[3]{9},\sqrt[4]{11},\sqrt[6]{17}$

$\because L.C.M$of 3, 4, 6 is 12

$\therefore\sqrt[3]{9} = 9^{1/3} = (9^{4})^{1/12} = (6561)^{1/12}$,

$\sqrt[4]{11} = (11)^{1/4}(11^{3})^{1/12} = (1331)^{1/12}$,

$\sqrt[6]{17} = (17)^{1/6} = (17^{2})^{1/2} = (289)^{1/12}$

Hence $\sqrt[3]{9}$is the greatest number.