List questions from nested-radicals

Published on 26 Mar 2026 - 11:47

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how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$

Published on 25 Aug 2012 - 6:56

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Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.

Published on 11 Sep 2012 - 8:00

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Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$

Published on 15 Sep 2012 - 14:00

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Justifying the procedure of computing $\sqrt{10+\sqrt{100+\sqrt{10,000 +\dots}}}$

Published on 22 Sep 2012 - 16:18

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Sum and Product of Infinite Radicals

Published on 23 Sep 2012 - 15:17

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How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$

Published on 18 Oct 2012 - 6:49

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Showing that $3 > \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} > 3-\frac{1}{5^{2011}}$ ($2012$ total square roots)

Published on 19 Nov 2012 - 15:59

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calculate the limit of this sequence $\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1..}}}}$

Published on 30 Dec 2012 - 9:10

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'Continued roots''

Published on 04 Jan 2013 - 11:36

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Prove $ \sqrt{1 + \sqrt[3]{2}} $ is irrational using the theorem about rational roots of a polynomial

Published on 10 Jan 2013 - 23:51

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Yet another nested radical

Published on 25 Mar 2026 - 18:58

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Square root of surds: $\sqrt{12+2\sqrt{6}}$?

Published on 03 Feb 2013 - 22:57

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Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$

Published on 11 Feb 2013 - 15:26

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Convergence of nested radicals

Published on 06 Mar 2013 - 16:17

List Question

Rationalize and simplify $\frac{x-1}{\sqrt{2\sqrt{x}} + 1 - \sqrt[4]{x}}$

how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$

Simplify $\sqrt {\sqrt[3]{5}-\sqrt[3]{4}}$.

Strategies to denest nested radicals $\sqrt{a+b\sqrt{c}}$

Justifying the procedure of computing $\sqrt{10+\sqrt{100+\sqrt{10,000 +\dots}}}$

Sum and Product of Infinite Radicals

How to solve this equation:$\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-5}}}}=5$

Showing that $3 > \sqrt{6+\sqrt{6+\sqrt{6+\cdots}}} > 3-\frac{1}{5^{2011}}$ ($2012$ total square roots)

calculate the limit of this sequence $\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1..}}}}$

'Continued roots''

Prove $ \sqrt{1 + \sqrt[3]{2}} $ is irrational using the theorem about rational roots of a polynomial

Yet another nested radical

Square root of surds: $\sqrt{12+2\sqrt{6}}$?

Evaluating $\sqrt{1 + \sqrt{2 + \sqrt{4 + \sqrt{8 + \ldots}}}}$

Convergence of nested radicals

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