List questions from rationality-testing

Published on 07 Apr 2016 - 21:35

437

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How to prove $\sqrt3 + \sqrt[3]{2}$ is a irrational number?

Published on 14 May 2016 - 15:59

187

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For which $a,b\in \mathbb{N},$ is $\frac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}}$ is a rational number.

Published on 18 May 2016 - 2:49

236

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Irrationality of $\min$ and $\arg\,\min$ of $\Gamma|_{[1, 2]}$

Published on 18 May 2016 - 13:08

43

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Proving that if $m,n,p,q\in\mathbb{Z^+}, \sqrt[p]{m}\in\mathbb{R}\setminus\mathbb{Q}$ then $\sqrt[p]{m}+\sqrt[q]{n}\in\mathbb{R}\setminus\mathbb{Q}$

Published on 25 May 2016 - 16:15

77

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Proving that things are or aren't rational numbers

Published on 31 May 2016 - 16:35

140

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Irrationality of the concatenation of the rightmost nonzero digits in $n!$

Published on 31 May 2016 - 19:11

323

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Proving that $\pi$ and $e$ are rational numbers

Published on 17 Jun 2016 - 9:07

159

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Why we square while doing the proof of √2 is irrational?

Published on 19 Jun 2016 - 12:06

155

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The $n$-th root of $(1+q^n)^2$ is irrational

Published on 26 Mar 2026 - 11:04

2.4k

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Is $\sqrt{2}^{\sqrt{2}}$ rational?

Published on 28 Jun 2016 - 11:01

119

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Is $\zeta(2n+1)\notin (2\pi)^{2n+1}\mathbb{Q}$ already known?

Published on 01 Jul 2016 - 21:48

116

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For any positive integers $a$ and $b$, what relation must hold between them to ensure that $\dfrac{a}{b}$ is an irrational number?

Published on 02 Jul 2016 - 16:06

1.7k

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How to prove to be an irrational number? Like $\sqrt{2}$, $\sqrt{3}$, or $\sum\limits_{k=1}^{\infty} \frac{1}{n^2}=\pi^2/6$

Published on 21 May 2013 - 14:46

22.4k

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Can $x^{x^{x^x}}$ be a rational number?

Published on 26 Mar 2026 - 14:29

List Question

How can I prove $\sqrt{\sqrt2}$ to be irrational?

How to prove $\sqrt3 + \sqrt[3]{2}$ is a irrational number?

For which $a,b\in \mathbb{N},$ is $\frac{\sqrt{2}+\sqrt{a}}{\sqrt{3}+\sqrt{b}}$ is a rational number.

Irrationality of $\min$ and $\arg\,\min$ of $\Gamma|_{[1, 2]}$

Proving that if $m,n,p,q\in\mathbb{Z^+}, \sqrt[p]{m}\in\mathbb{R}\setminus\mathbb{Q}$ then $\sqrt[p]{m}+\sqrt[q]{n}\in\mathbb{R}\setminus\mathbb{Q}$

Proving that things are or aren't rational numbers

Irrationality of the concatenation of the rightmost nonzero digits in $n!$

Proving that $\pi$ and $e$ are rational numbers

Why we square while doing the proof of √2 is irrational?

The $n$-th root of $(1+q^n)^2$ is irrational

Is $\sqrt{2}^{\sqrt{2}}$ rational?

Is $\zeta(2n+1)\notin (2\pi)^{2n+1}\mathbb{Q}$ already known?

For any positive integers $a$ and $b$, what relation must hold between them to ensure that $\dfrac{a}{b}$ is an irrational number?

How to prove to be an irrational number? Like $\sqrt{2}$, $\sqrt{3}$, or $\sum\limits_{k=1}^{\infty} \frac{1}{n^2}=\pi^2/6$

Can $x^{x^{x^x}}$ be a rational number?

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