The greatest one of 2 , 3 3 , 6 6 , 5 5 is = ?

Answer: Option B

$$\begin{array}{rl}& \sqrt{2}\to 2^{\frac{1}{2}}\to 2^{\frac{15}{30}}=\text{root}30\text{of}{2}^{15}=\text{root}30\text{of}32768\\ & \text{root}3\text{of}3\to 3^{\frac{1}{3}}\to 3^{\frac{10}{30}}=\text{root}30\text{of}{3}^{10}=\text{root}30\text{of}59049\\ & \text{root}6\text{of}6\to 6^{\frac{1}{6}}\to 6^{\frac{5}{30}}=\text{root}30\text{of}{6}^5=\text{root}30\text{of}7776\\ & \text{root}5\text{of}5\to 5^{\frac{1}{5}}\to 5^{\frac{6}{30}}=\text{root}30\text{of}{5}^6=\text{root}30\text{of}15625\\ & \text{So }\text{root}3\text{of}3\text{ is the greatest}\text{.}\end{array}$$