Question

A sequence of nested radicals and its limit

score 627 · Answer 1 · 2026-04-30 02:59:45

627

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A sequence of nested radicals and its limit

Published on 30 Apr 2026 - 2:59

score 114 · Answer 2 · 2026-05-05 13:57:10

114

Views

Prove that this formulae equals 3

Published on 05 May 2026 - 13:57

score 619 · Answer 3 · 2026-05-04 18:53:04

619

Views

Alternate proof for Viète's infinite product of nested radicals

Published on 04 May 2026 - 18:53

score 137 · Answer 4 · 2026-04-29 14:06:17

137

Views

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

Published on 29 Apr 2026 - 14:06

score 88 · Answer 5 · 2026-04-30 03:42:47

88

Views

Simplification via Denesting Radicals

Published on 30 Apr 2026 - 3:42

score 203 · Answer 6 · 2026-04-29 17:11:23

203

Views

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

Published on 29 Apr 2026 - 17:11

score 128 · Answer 7 · 2026-05-07 16:53:37

128

Views

Exclusive way to solve irrational equation

Published on 07 May 2026 - 16:53

score 570 · Answer 8 · 2026-04-29 23:41:47

570

Views

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

Published on 29 Apr 2026 - 23:41

score 140 · Answer 9 · 2026-05-07 10:45:41

140

Views

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

Published on 07 May 2026 - 10:45

score 241 · Answer 10 · 2026-04-29 14:09:32

241

Views

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

Published on 29 Apr 2026 - 14:09

score 202 · Answer 11 · 2026-05-02 05:19:11

202

Views

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

Published on 02 May 2026 - 5:19

score 321 · Answer 12 · 2026-05-07 16:53:25

321

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 07 May 2026 - 16:53

score 458 · Answer 13 · 2026-04-18 00:44:48

458

Views

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

Published on 18 Apr 2026 - 0:44

score 120 · Answer 14 · 2026-04-18 16:22:39

120

Views

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

Published on 18 Apr 2026 - 16:22

score 337 · Answer 15 · 2026-04-18 11:28:29

337

Views

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

Published on 18 Apr 2026 - 11:28

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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