List questions from rationality-testing

Published on 21 Jul 2017 - 6:06

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Monty Hall Problem - Extended

Published on 26 Mar 2026 - 1:17

242

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Is $\sum_{n\ge0}\frac1{2^{2^n}}$ rational?

Published on 02 Aug 2017 - 1:17

243

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Rational value of sine

Published on 21 Aug 2017 - 3:14

291

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Prove that an infinite decimal whose digits are natural numbers strung end to end is irrational

Published on 26 Aug 2017 - 6:49

180

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Prove that $1+3^{\frac{1}{5}}+3^{\frac{2}{5}}+3^{\frac{3}{5}}+3^{\frac{4}{5}}$ is irrational

Published on 01 Nov 2017 - 1:44

327

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Show that there are no rationals $r$ such that $r^3 = 6$

Published on 08 Nov 2017 - 17:31

551

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Is $n^\frac{1}{n}$ ever rational?

Published on 25 Nov 2017 - 13:37

213

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Show that $\sqrt{2} \notin \mathbb{Q}(i)$ using infinite descent

Published on 27 Feb 2026 - 11:01

1.5k

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Irrationality of $\pi^2$ and $\pi^3$

Published on 29 Dec 2017 - 21:07

26.2k

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How can you prove that the square root of two is irrational?

Published on 20 Jul 2010 - 19:18

45.8k

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How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

Published on 24 Feb 2026 - 1:52

9k

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Is $n^{th}$ root of $2$ an irrational number?

Published on 25 Nov 2010 - 19:43

8.5k

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Irrationality proofs not by contradiction

Published on 05 Feb 2011 - 18:55

2.9k

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Is there an alternative proof for periodic expansion of decimal fraction?

Published on 25 Apr 2011 - 23:45

List Question

Prove the series $\sum_{n=1}^{\infty}\frac{1}{{5^n}^!}$ converges to an irrational number

Monty Hall Problem - Extended

Is $\sum_{n\ge0}\frac1{2^{2^n}}$ rational?

Rational value of sine

Prove that an infinite decimal whose digits are natural numbers strung end to end is irrational

Prove that $1+3^{\frac{1}{5}}+3^{\frac{2}{5}}+3^{\frac{3}{5}}+3^{\frac{4}{5}}$ is irrational

Show that there are no rationals $r$ such that $r^3 = 6$

Is $n^\frac{1}{n}$ ever rational?

Show that $\sqrt{2} \notin \mathbb{Q}(i)$ using infinite descent

Irrationality of $\pi^2$ and $\pi^3$

How can you prove that the square root of two is irrational?

How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?

Is $n^{th}$ root of $2$ an irrational number?

Irrationality proofs not by contradiction

Is there an alternative proof for periodic expansion of decimal fraction?

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