The value of 2 3 4 2 3 4 ...... is?

Answer: Option A

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