Question

A sequence of nested radicals and its limit

score 622 · Answer 1 · 2026-03-22 11:39:06

622

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A sequence of nested radicals and its limit

Published on 22 Mar 2026 - 11:39

score 105 · Answer 2 · 2026-03-17 14:27:24

105

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Prove that this formulae equals 3

Published on 17 Mar 2026 - 14:27

score 611 · Answer 3 · 2026-03-17 20:52:09

611

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Alternate proof for Viète's infinite product of nested radicals

Published on 17 Mar 2026 - 20:52

score 129 · Answer 4 · 2026-03-22 13:43:18

129

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Is what I have got about $\int\sqrt{x+\left(\sqrt{{x}+\sqrt{x+\cdots}}\right)}dx$ true or false?

Published on 22 Mar 2026 - 13:43

score 83 · Answer 5 · 2026-03-22 06:21:50

83

Views

Simplification via Denesting Radicals

Published on 22 Mar 2026 - 6:21

score 196 · Answer 6 · 2026-03-20 02:57:02

196

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Proof that $\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{1+2(\ldots)}}}} = 1+\sqrt{2}$

Published on 20 Mar 2026 - 2:57

score 120 · Answer 7 · 2026-03-22 12:41:33

120

Views

Exclusive way to solve irrational equation

Published on 22 Mar 2026 - 12:41

score 563 · Answer 8 · 2026-03-20 12:10:14

563

Views

What is the value of $\sqrt{1+ \sqrt[3]{1+\sqrt[4]{1+ \sqrt[5]{1+ \cdots }}}}$?

Published on 20 Mar 2026 - 12:10

score 130 · Answer 9 · 2026-03-22 08:25:37

130

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Simplification of radicals: $\sqrt{4+\sqrt5}-\sqrt{\frac{4+\sqrt{11}}{2}}$

Published on 22 Mar 2026 - 8:25

score 233 · Answer 10 · 2026-03-22 05:19:25

233

Views

Simplifying nested radicals? $\left(\sqrt{4+\sqrt{16-a^2}}+\sqrt{4-\sqrt{16-a^2}}\right)^2$

Published on 22 Mar 2026 - 5:19

score 195 · Answer 11 · 2026-03-20 01:00:29

195

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On $3+\sqrt{11+\sqrt{11+\sqrt{11+\sqrt{11+\dots}}}}=\phi^4$ and friends

Published on 20 Mar 2026 - 1:00

score 318 · Answer 12 · 2026-03-25 04:42:53

318

Views

Find the rational number of a, b, c, solving $\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{a}+ \sqrt[3]{b}+\sqrt[3]{c}$

Published on 25 Mar 2026 - 4:42

score 456 · Answer 13 · 2026-03-25 03:03:45

456

Views

Use Ramanujan’s method to denest $\sqrt[3]{7\sqrt[3]{20}-1}$ and $\sqrt[3]{7\sqrt[3]{20}-19}$

Published on 25 Mar 2026 - 3:03

score 116 · Answer 14 · 2026-03-25 06:01:16

116

Views

How is this nested radical expression for $\cos(2\pi /7)$ proven?

Published on 25 Mar 2026 - 6:01

score 333 · Answer 15 · 2026-03-25 04:42:56

333

Views

If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$?

Published on 25 Mar 2026 - 4:42

List Question

A sequence of nested radicals and its limit

Prove that this formulae equals 3

Alternate proof for Viète's infinite product of nested radicals

Is what I have got about $\int\sqrt{x+\left(\sqrt{{x}+\sqrt{x+\cdots}}\right)}dx$ true or false?

Simplification via Denesting Radicals

Proof that $\sqrt{1+2\sqrt{1+2\sqrt{1+2\sqrt{1+2(\ldots)}}}} = 1+\sqrt{2}$

Exclusive way to solve irrational equation

What is the value of $\sqrt{1+ \sqrt[3]{1+\sqrt[4]{1+ \sqrt[5]{1+ \cdots }}}}$?

Simplification of radicals: $\sqrt{4+\sqrt5}-\sqrt{\frac{4+\sqrt{11}}{2}}$

Simplifying nested radicals? $\left(\sqrt{4+\sqrt{16-a^2}}+\sqrt{4-\sqrt{16-a^2}}\right)^2$

On $3+\sqrt{11+\sqrt{11+\sqrt{11+\sqrt{11+\dots}}}}=\phi^4$ and friends

Find the rational number of a, b, c, solving $\sqrt[3]{\sqrt[3]{2}-1}=\sqrt[3]{a}+ \sqrt[3]{b}+\sqrt[3]{c}$

Use Ramanujan’s method to denest $\sqrt[3]{7\sqrt[3]{20}-1}$ and $\sqrt[3]{7\sqrt[3]{20}-19}$

How is this nested radical expression for $\cos(2\pi /7)$ proven?

If $f(x)^2=x+(x+1)f(x+2)$, what is $f(1)$?

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