Question

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

score 289 · Answer 1 · 2026-03-29 15:02:30

289

Views

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

Published on 29 Mar 2026 - 15:02

score 156 · Answer 2 · 2015-07-28 12:37:41

156

Views

Is the inequality $| \sqrt[3]{x^2} - \sqrt[3]{y^2} | \le \sqrt[3]{|x -y|^2}$ true?

Published on 28 Jul 2015 - 12:37

score 978 · Answer 3 · 2015-07-28 12:50:42

978

Views

find x in $\sqrt[3]{6+\sqrt x} + \sqrt[3]{6-\sqrt x} = \sqrt[3] {3}$

Published on 28 Jul 2015 - 12:50

score 175 · Answer 4 · 2015-07-29 15:25:56

175

Views

Solve the equation $4\sqrt{2-x^2}=-x^3-x^2+3x+3$

Published on 29 Jul 2015 - 15:25

score 3.4k · Answer 5 · 2026-04-04 15:21:31

3.4k

Views

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

Published on 04 Apr 2026 - 15:21

score 166 · Answer 6 · 2015-07-31 09:00:22

166

Views

A basic root numbers question

Published on 31 Jul 2015 - 9:00

score 61 · Answer 7 · 2015-08-02 13:26:34

61

Views

Two infinite radicals question

Published on 02 Aug 2015 - 13:26

score 136 · Answer 8 · 2026-02-24 19:05:36

136

Views

Find the approximate square root of $(a^4-a^{-4})/(a^2-a^{-2})$

Published on 24 Feb 2026 - 19:05

score 2.1k · Answer 9 · 2026-03-26 19:11:54

2.1k

Views

$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.

Published on 26 Mar 2026 - 19:11

score 136 · Answer 10 · 2026-04-02 11:26:30

136

Views

Are there expansions of the expression $(a+b)^{1/n}$?

Published on 02 Apr 2026 - 11:26

score 945 · Answer 11 · 2015-08-05 08:25:36

945

Views

Why does $x^2+47y^2 = z^5$ involve solvable quintics?

Published on 05 Aug 2015 - 8:25

score 654 · Answer 12 · 2015-08-05 08:33:04

654

Views

Proving $\sum_{j=1}^n \frac{1}{\sqrt{j}} > \sqrt{n}$ with induction

Published on 05 Aug 2015 - 8:33

score 1.1k · Answer 13 · 2015-08-05 15:56:51

1.1k

Views

Radical under Radical expression

Published on 05 Aug 2015 - 15:56

score 66 · Answer 14 · 2015-08-06 15:20:28

66

Views

Take $\sqrt[n]{m}$ where $n$ is a positive non-integer number. Is this possible?

Published on 06 Aug 2015 - 15:20

score 74 · Answer 15 · 2015-08-07 20:04:44

74

Views

Solving algebraic equations with radicals: $x(x-\sqrt3)(x+1)+3-\sqrt3=0$

Published on 07 Aug 2015 - 20:04

List Question

Proposition: $\sqrt{x + \sqrt{x + \sqrt{x + ...}}} = \frac{1 + \sqrt{1 + 4x}}{2}$.

Is the inequality $| \sqrt[3]{x^2} - \sqrt[3]{y^2} | \le \sqrt[3]{|x -y|^2}$ true?

find x in $\sqrt[3]{6+\sqrt x} + \sqrt[3]{6-\sqrt x} = \sqrt[3] {3}$

Solve the equation $4\sqrt{2-x^2}=-x^3-x^2+3x+3$

The value of the integral $\int_0^2\left(\sqrt{1+x^3}+\sqrt[3]{x^2+2x}\:\right)dx$

A basic root numbers question

Two infinite radicals question

Find the approximate square root of $(a^4-a^{-4})/(a^2-a^{-2})$

$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.

Are there expansions of the expression $(a+b)^{1/n}$?

Why does $x^2+47y^2 = z^5$ involve solvable quintics?

Proving $\sum_{j=1}^n \frac{1}{\sqrt{j}} > \sqrt{n}$ with induction

Radical under Radical expression

Take $\sqrt[n]{m}$ where $n$ is a positive non-integer number. Is this possible?

Solving algebraic equations with radicals: $x(x-\sqrt3)(x+1)+3-\sqrt3=0$

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