Question

Proof for an equality involving square roots

score 394 · Answer 1 · 2013-03-22 17:54:02

394

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Proof for an equality involving square roots

Published on 22 Mar 2013 - 17:54

score 259 · Answer 2 · 2020-08-02 22:17:23

259

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How would I simplify this function $\rho(x)=x+\sqrt{x-\sqrt{x-\sqrt{x+\sqrt{\dots}}}}$

Published on 02 Aug 2020 - 22:17

score 95 · Answer 3 · 2020-08-09 09:33:24

95

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An analogue to Ramanujan's identity $\left\{3\left(\left(a^{3}+b^{3}\right)^{1/3}-a\right)\left(\left(a^{3}+b^{3}\right)^{1/3}-b\right)\right\}^{1/3}$

Published on 09 Aug 2020 - 9:33

score 65 · Answer 4 · 2026-03-30 16:09:55

65

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How to get rid of such radicals?

Published on 30 Mar 2026 - 16:09

score 82 · Answer 5 · 2020-08-31 17:46:54

82

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Simplify a radical inside a radical inside a radical

Published on 31 Aug 2020 - 17:46

score 44 · Answer 6 · 2020-08-31 17:55:43

44

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Infinite nested radical with variables

Published on 31 Aug 2020 - 17:55

score 252 · Answer 7 · 2020-09-02 17:22:03

252

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Does a value for $\sqrt{x+\sqrt{x+\sqrt{x+...}}}$ actually exist?

Published on 02 Sep 2020 - 17:22

score 608 · Answer 8 · 2020-09-06 13:57:08

608

Views

Alternate method to solve $\sqrt{11\sqrt{11\sqrt{11...4\, \text{times}}}}$

Published on 06 Sep 2020 - 13:57

score 406 · Answer 9 · 2020-09-08 22:03:31

406

Views

Solving infinite nested square roots of 2 converging to finite nested radical

Published on 08 Sep 2020 - 22:03

score 86 · Answer 10 · 2020-09-12 18:05:31

86

Views

Is $\sqrt[3]{24+\sqrt[3]{24+\sqrt[3]{24+\cdots}}}$ even? prime? composite? an even prime?

Published on 12 Sep 2020 - 18:05

score 99 · Answer 11 · 2026-03-27 14:02:29

99

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Find value of $\sin x-\frac{1}{\cot x}$

Published on 27 Mar 2026 - 14:02

score 39 · Answer 12 · 2020-09-24 08:19:03

39

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Prove the convergence of the infinite product involving nested radicals

Published on 24 Sep 2020 - 8:19

score 847 · Answer 13 · 2020-09-26 20:55:59

847

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Solving cyclic infinite nested square roots of 2 as cosine functions

Published on 26 Sep 2020 - 20:55

score 215 · Answer 14 · 2020-09-27 04:27:39

215

Views

Simplify $(1+\sqrt{3}) \cdot \sqrt{2-\sqrt{3}}$

Published on 27 Sep 2020 - 4:27

score 801 · Answer 15 · 2026-03-26 01:23:33

801

Views

$\sqrt{a^2+5b^2}+\sqrt{b^2+5c^2}+\sqrt{c^2+5a^2}\geq\sqrt{10(a^2+b^2+c^2)+8(ab+ac+bc)}$ for any real numbers.

Published on 26 Mar 2026 - 1:23

List Question

Proof for an equality involving square roots

How would I simplify this function $\rho(x)=x+\sqrt{x-\sqrt{x-\sqrt{x+\sqrt{\dots}}}}$

An analogue to Ramanujan's identity $\left\{3\left(\left(a^{3}+b^{3}\right)^{1/3}-a\right)\left(\left(a^{3}+b^{3}\right)^{1/3}-b\right)\right\}^{1/3}$

How to get rid of such radicals?

Simplify a radical inside a radical inside a radical

Infinite nested radical with variables

Does a value for $\sqrt{x+\sqrt{x+\sqrt{x+...}}}$ actually exist?

Alternate method to solve $\sqrt{11\sqrt{11\sqrt{11...4\, \text{times}}}}$

Solving infinite nested square roots of 2 converging to finite nested radical

Is $\sqrt[3]{24+\sqrt[3]{24+\sqrt[3]{24+\cdots}}}$ even? prime? composite? an even prime?

Find value of $\sin x-\frac{1}{\cot x}$

Prove the convergence of the infinite product involving nested radicals

Solving cyclic infinite nested square roots of 2 as cosine functions

Simplify $(1+\sqrt{3}) \cdot \sqrt{2-\sqrt{3}}$

$\sqrt{a^2+5b^2}+\sqrt{b^2+5c^2}+\sqrt{c^2+5a^2}\geq\sqrt{10(a^2+b^2+c^2)+8(ab+ac+bc)}$ for any real numbers.

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