Q. 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) Cannot be determined
Explanation
(a)
$\because$ LCM of 3, 4, 6 is 12.
$\therefore\ \ \ \sqrt[3]{9} = 9^{1/3} = \left( 9^{4} \right)^{1/12} = (6561)^{1/12}$
$\sqrt[4]{11} = (11)^{1/4} = \left( 11^{3} \right)^{1/12} = (1331)^{1/12}$
$\sqrt[6]{17} = (17)^{1/6} = \left( 17^{2} \right)^{1/2} = (289)^{1/12}$
Hence, $\sqrt[3]{9}$ is the greatest number.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.