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Question Number 172262 by Mikenice last updated on 25/Jun/22

Answered by Rasheed.Sindhi last updated on 25/Jun/22

$$\sqrt[3]{3\sqrt[3]{3\sqrt[3]{3...}}}=\sqrt{n}>0$$$${\left(\sqrt[3]{3\sqrt[3]{3\sqrt[3]{3...}}}\right)}^3={\left(\sqrt{n}\right)}^3$$$$3\sqrt[3]{3\sqrt[3]{3...}}={\left(\sqrt{n}\right)}^3$$$$3\sqrt{n}={\left(\sqrt{n}\right)}^3$$$$3={\left(\sqrt{n}\right)}^2;n\ne 0$$$$n=3$$

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