The value of $$\sqrt {2\root 3 \of {4\sqrt {2\root 3 \of 4 } } } ......$$    is?

Solution (By Examveda Team)

$$\eqalign{ & x = \sqrt {2\root 3 \of {4\sqrt {2\root 3 \of 4 } } } ...... \cr & {\text{Squaring both side}} \cr & \Rightarrow {x^2} = 2\root 3 \of {4\sqrt {2\root 3 \of 4 } } ...... \cr & {\text{Now cubing both sides}} \cr & \Rightarrow {x^6} = 8 \times 4x \cr & \Rightarrow {x^5} = 32 \cr & \Rightarrow {x^5} = {2^5} \cr & \Rightarrow x = 2 \cr} $$