# Aptitude Question ID : 92817

The greatest among the following numbers
$(3)^{\frac{1}{3}}, (2)^{\frac{1}{2}}, 1, (6)^{\frac{1}{6}}$
[A] $1$
[B]$(2)^{\frac{1}{2}}$
[C]$(3)^{\frac{1}{3}}$
[D]$(6)^{\frac{1}{6}}$

$\mathbf{(3)^{\frac{1}{3}}}$
LCM of 3, 2 and 6 = 6
$\therefore (3)^{\frac{1}{3}} = (3^{2})^{\frac{1}{6}} = (9)^{\frac{1}{6}}$
$(2)^{\frac{1}{2}} = (2^{3})^{\frac{1}{6}} = (8)^{\frac{1}{6}}$
$(1)^\frac{1}{6} = 1$
$(6)^\frac{1}{6} = (6)^\frac{1}{6}$
Hence option [C] is the right answer.