List questions from nested-radicals

Published on 19 Jul 2014 - 10:37

148

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A problem on nested radicals

Published on 22 Jul 2014 - 11:04

238

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Find the exact value of expression $S=\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+\sqrt[6]{4+\cdots}}}}}$

Published on 22 Jul 2014 - 21:38

496

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Find the value of this infinitely nested radical (it appears to obtain multiple values)

Published on 24 Jul 2014 - 20:36

308

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Evaluating an infinite square root

Published on 25 Jul 2014 - 23:47

414

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An incorrect answer for an integral

Published on 27 Jul 2014 - 14:10

467

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Equality of two iterated square roots

Published on 05 Aug 2014 - 13:34

289

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Simplifying $\sqrt[3]{a\pm\sqrt{b}}$

Published on 14 Aug 2014 - 10:35

4.1k

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Is $\sqrt {2 \sqrt {3 \sqrt {4 \ldots}}}$ algebraic or transcendental?

Published on 13 Mar 2026 - 5:42

1.7k

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Where did the negative answer come from?

Published on 16 Aug 2014 - 8:19

471

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Denest $\sqrt{\left(2+\sqrt{2}\right) \left(10-2 \sqrt{5}\right)}$

Published on 21 Aug 2014 - 10:52

245

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Closed formula for the numbers of the form $\sqrt{1+\sqrt{4+\sqrt{9}}}$

Published on 21 Aug 2014 - 11:14

802

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Nested Radicals with multiplication

Published on 22 Aug 2014 - 11:29

362

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Find the value of : $\lim_{n\rightarrow \infty}\sqrt{2+\sqrt{2+\sqrt{...+\sqrt{2}}}}$

Published on 23 Aug 2014 - 19:45

180

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Let $\alpha > 0$, use mathematical induction to prove that

Published on 03 Sep 2014 - 10:48

List Question

Denesting radicals like $\sqrt[3]{\sqrt[3]{2} - 1}$

A problem on nested radicals

Find the exact value of expression $S=\sqrt{4+\sqrt[3]{4+\sqrt[4]{4+\sqrt[5]{4+\sqrt[6]{4+\cdots}}}}}$

Find the value of this infinitely nested radical (it appears to obtain multiple values)

Evaluating an infinite square root

An incorrect answer for an integral

Equality of two iterated square roots

Simplifying $\sqrt[3]{a\pm\sqrt{b}}$

Is $\sqrt {2 \sqrt {3 \sqrt {4 \ldots}}}$ algebraic or transcendental?

Where did the negative answer come from?

Denest $\sqrt{\left(2+\sqrt{2}\right) \left(10-2 \sqrt{5}\right)}$

Closed formula for the numbers of the form $\sqrt{1+\sqrt{4+\sqrt{9}}}$

Nested Radicals with multiplication

Find the value of : $\lim_{n\rightarrow \infty}\sqrt{2+\sqrt{2+\sqrt{...+\sqrt{2}}}}$

Let $\alpha > 0$, use mathematical induction to prove that

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