Question

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

score 98 · Answer 1 · 2026-04-17 08:49:12

98

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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 17 Apr 2026 - 8:49

score 26 · Answer 2 · 2026-04-11 14:18:15

26

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How to derive this particular fraction with roots from another

Published on 11 Apr 2026 - 14:18

score 85 · Answer 3 · 2026-04-17 11:26:37

85

Views

Why $\sqrt{\left(\frac{-\sqrt3}2\right)^2+{(\frac12)}^2}$ is equal to 1?

Published on 17 Apr 2026 - 11:26

score 299 · Answer 4 · 2026-04-17 04:23:22

299

Views

Closed form of hypergeometric $\, _4F_3\left(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8};\frac{5}{6},\frac{7}{6},\frac{9}{6};z\right)$

Published on 17 Apr 2026 - 4:23

score 118 · Answer 5 · 2026-04-10 20:03:48

118

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Integration with surds, problem taking out $x^2$

Published on 10 Apr 2026 - 20:03

score 313 · Answer 6 · 2026-04-11 10:58:24

313

Views

Jacobson radical of Polynomial ring

Published on 11 Apr 2026 - 10:58

score 65 · Answer 7 · 2026-04-11 10:24:25

65

Views

Precalculus algebra problem about rational and irrational numbers.

Published on 11 Apr 2026 - 10:24

score 581 · Answer 8 · 2026-04-16 02:55:54

581

Views

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Published on 16 Apr 2026 - 2:55

score 61 · Answer 9 · 2026-04-10 01:24:54

61

Views

Is squaring of both sides of this equation allowed?

Published on 10 Apr 2026 - 1:24

score 67 · Answer 10 · 2026-04-09 15:47:21

67

Views

How to get rid of such radicals?

Published on 09 Apr 2026 - 15:47

score 66 · Answer 11 · 2026-04-17 16:51:31

66

Views

When its possible to write a number $a+b\sqrt{c}$ as the square of a sum?

Published on 17 Apr 2026 - 16:51

score 166 · Answer 12 · 2026-04-15 13:02:34

166

Views

If $(a-b^2)b>0$, then $\sqrt[3]{a+\frac{9b^3+a}{3b}\sqrt{\frac{a-b^3}{3b}}}+\sqrt[3]{a-\frac{9b^3+a}{3b}\sqrt{\frac{a-b^3}{3b}}}$ is rational

Published on 15 Apr 2026 - 13:02

score 97 · Answer 13 · 2026-04-16 21:18:46

97

Views

Solving the equation $\sqrt{x+2} + \sqrt{4x+1} = 5$.

Published on 16 Apr 2026 - 21:18

score 68 · Answer 14 · 2026-04-16 19:12:33

68

Views

Simplifying $\frac{\frac12\sqrt{w^2+d^2}}{\sqrt{\frac14(w^2+d^2)+(h-k)^2}}$ to $\sqrt{\frac{w^2+d^2}{d^2+4(h-k)^2+w^2}}$

Published on 16 Apr 2026 - 19:12

score 85 · Answer 15 · 2026-04-12 11:12:37

85

Views

Simplify a radical inside a radical inside a radical

Published on 12 Apr 2026 - 11:12

List Question

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 derive this particular fraction with roots from another

Why $\sqrt{\left(\frac{-\sqrt3}2\right)^2+{(\frac12)}^2}$ is equal to 1?

Closed form of hypergeometric $\, _4F_3\left(\frac{3}{8},\frac{5}{8},\frac{7}{8},\frac{9}{8};\frac{5}{6},\frac{7}{6},\frac{9}{6};z\right)$

Integration with surds, problem taking out $x^2$

Jacobson radical of Polynomial ring

Precalculus algebra problem about rational and irrational numbers.

Given a field $\mathbb F$, is there a smallest field $\mathbb G\supseteq\mathbb F$ where every element in $\mathbb G$ has an $n$th root for all $n$?

Is squaring of both sides of this equation allowed?

How to get rid of such radicals?

When its possible to write a number $a+b\sqrt{c}$ as the square of a sum?

If $(a-b^2)b>0$, then $\sqrt[3]{a+\frac{9b^3+a}{3b}\sqrt{\frac{a-b^3}{3b}}}+\sqrt[3]{a-\frac{9b^3+a}{3b}\sqrt{\frac{a-b^3}{3b}}}$ is rational

Solving the equation $\sqrt{x+2} + \sqrt{4x+1} = 5$.

Simplifying $\frac{\frac12\sqrt{w^2+d^2}}{\sqrt{\frac14(w^2+d^2)+(h-k)^2}}$ to $\sqrt{\frac{w^2+d^2}{d^2+4(h-k)^2+w^2}}$

Simplify a radical inside a radical inside a radical

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