√7√7√7√7√7⋯\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}} approximation [closed]

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Is there any trick to evaluate this or this is an approximation, I mean I am not allowed to use calculator.

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

Answer

$\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7...}}}}}=7^\frac{1}{2}\cdot7^\frac{1}{4}\cdot 7^\frac{1}{8}\cdots=7^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\cdots}=7^{\frac{\frac{1}{2}}{1-\frac{1}{2}}}=7$

Attribution
Source : Link , Question Author : user2378 , Answer Author : Madrit Zhaku

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