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Question Number 34408 by Rio Mike last updated on 05/May/18

$$whatisthevalueof$$$$\sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{5}}}}}}$$$$ignoring64.$$

Commented by candre last updated on 06/May/18

$$x=\sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{5}}}}}}$$$$x^2=5\sqrt{5\sqrt{5\sqrt{5\sqrt{5\sqrt{5}}}}}$$$$x^4=5^3\sqrt{5\sqrt{5\sqrt{5\sqrt{5}}}}$$$$x^8=5^7\sqrt{5\sqrt{5\sqrt{5}}}$$$$x^{16}=5^{15}\sqrt{5\sqrt{5}}$$$$x^{32}=5^{31}\sqrt{5}$$$$x^{64}=5^{63}$$$$x=5^{\frac{63}{64}}$$

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