$\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation Is there any trick to evaluate this or this is an approximation, I mean I am not allowed to use calculator.

$$\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$$


$$x = \sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$$
$$x = \sqrt{7x}$$
$$x^2 - 7x = 0$$
$$x(x - 7) =0 \implies x = 7$$
Because $\sqrt{7} > 0$ we reject the $x=0$ solution.
