Question

Piecewise function with $\sqrt{2 + \sqrt{n}}$ and $\sqrt{1 + \frac{\sqrt{n}}{2}} + i \sqrt{-1 + \frac{\sqrt{n}}{2}}$

score 222 · Answer 1 · 2023-05-17 19:59:23

222

Views

Piecewise function with $\sqrt{2 + \sqrt{n}}$ and $\sqrt{1 + \frac{\sqrt{n}}{2}} + i \sqrt{-1 + \frac{\sqrt{n}}{2}}$

Published on 17 May 2023 - 19:59

score 103 · Answer 2 · 2023-05-23 23:46:32

103

Views

solutions to $x = \sqrt{a+\sqrt{a+\sqrt{a+\cdots}}}\;\;(\text{mod}\;p)$

Published on 23 May 2023 - 23:46

score 160 · Answer 3 · 2023-05-24 16:37:30

160

Views

Find the square root of the following binomial surd: $\sqrt{27}+2\sqrt{6}$

Published on 24 May 2023 - 16:37

score 806 · Answer 4 · 2023-05-24 20:54:59

806

Views

What is the simple way to solve the equation $x+\sqrt{a+\sqrt{x}}=a$ for all real $x$?

Published on 24 May 2023 - 20:54

score 91 · Answer 5 · 2026-03-26 14:34:59

91

Views

Nested radicals $\sqrt{C+1+b\sqrt{C+1+b^{2}\sqrt{C+1+b^{3}\sqrt{\cdot\cdot\cdot}}}}=g(x)$ then $\lim_{x\to\infty}(g(x+1)-g(x))=^?1$

Published on 26 Mar 2026 - 14:34

score 129 · Answer 6 · 2023-06-06 01:38:33

129

Views

A very interesting integral: $\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$

Published on 06 Jun 2023 - 1:38

score 194 · Answer 7 · 2023-06-14 11:48:16

194

Views

How to find the maximum value of $x^2-\frac {1}{x^2}$ if the real number $x$ satisfies $x^3-\frac{1}{x^3}=\frac {28}{27}$

Published on 14 Jun 2023 - 11:48

score 150 · Answer 8 · 2023-06-16 20:19:09

150

Views

Can the nested radicals in this expression be simplified?

Published on 16 Jun 2023 - 20:19

score 83 · Answer 9 · 2026-03-26 08:23:13

83

Views

Mixing Continued fraction and nested radicals does $D=-\pi+\ln(16)+(7\ln\pi)/2-7/3\arctan(\pi)$?

Published on 26 Mar 2026 - 8:23

score 203 · Answer 10 · 2023-07-30 10:56:41

203

Views

How does $\sqrt[6]{26+15\sqrt3}-\sqrt[6]{26-15\sqrt3}$ become $\sqrt2$?

Published on 30 Jul 2023 - 10:56

score 146 · Answer 11 · 2023-08-08 10:43:44

146

Views

Calculating $\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{100\;\text{times}}$ without a calculator?

Published on 08 Aug 2023 - 10:43

score 280 · Answer 12 · 2023-08-22 09:33:26

280

Views

Show $\frac{\pi^2}{6}\sqrt{ab+\sqrt{ab+2\sqrt{ab+3\sqrt{\cdots}}}}>4$ by hand .

Published on 22 Aug 2023 - 9:33

score 239 · Answer 13 · 2023-09-11 06:25:02

239

Views

Find the fourth roots of the following binomial surd: $14+8\sqrt{3}$

Published on 11 Sep 2023 - 6:25

score 21 · Answer 14 · 2026-03-26 16:03:52

21

Views

A Nested Radical Arising from a Nonlinear Recurrence

Published on 26 Mar 2026 - 16:03

score 43 · Answer 15 · 2026-03-26 17:29:47

43

Views

How do we prove this nested radical solution?

Published on 26 Mar 2026 - 17:29

List Question

Piecewise function with $\sqrt{2 + \sqrt{n}}$ and $\sqrt{1 + \frac{\sqrt{n}}{2}} + i \sqrt{-1 + \frac{\sqrt{n}}{2}}$

solutions to $x = \sqrt{a+\sqrt{a+\sqrt{a+\cdots}}}\;\;(\text{mod}\;p)$

Find the square root of the following binomial surd: $\sqrt{27}+2\sqrt{6}$

What is the simple way to solve the equation $x+\sqrt{a+\sqrt{x}}=a$ for all real $x$?

Nested radicals $\sqrt{C+1+b\sqrt{C+1+b^{2}\sqrt{C+1+b^{3}\sqrt{\cdot\cdot\cdot}}}}=g(x)$ then $\lim_{x\to\infty}(g(x+1)-g(x))=^?1$

A very interesting integral: $\int\limits^{2}_{1}\sqrt{x-\sqrt{x!-\sqrt{(x!)!-\sqrt{((x!)!)!-\dots}}}}dx$

How to find the maximum value of $x^2-\frac {1}{x^2}$ if the real number $x$ satisfies $x^3-\frac{1}{x^3}=\frac {28}{27}$

Can the nested radicals in this expression be simplified?

Mixing Continued fraction and nested radicals does $D=-\pi+\ln(16)+(7\ln\pi)/2-7/3\arctan(\pi)$?

How does $\sqrt[6]{26+15\sqrt3}-\sqrt[6]{26-15\sqrt3}$ become $\sqrt2$?

Calculating $\underbrace{\sqrt{2+\sqrt{2+\sqrt{2+\cdots +\sqrt{2}}}}}_{100\;\text{times}}$ without a calculator?

Show $\frac{\pi^2}{6}\sqrt{ab+\sqrt{ab+2\sqrt{ab+3\sqrt{\cdots}}}}>4$ by hand .

Find the fourth roots of the following binomial surd: $14+8\sqrt{3}$

A Nested Radical Arising from a Nonlinear Recurrence

How do we prove this nested radical solution?

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