List questions from rationality-testing

Published on 25 Mar 2026 - 12:53

103

Views

A simple proof for non-rationality of number $\sqrt[n]{1+q^n}$

Published on 06 Aug 2016 - 13:32

1.3k

Views

Shorter proof of irrationality of $\sqrt{2}$?

Published on 07 Aug 2016 - 12:36

937

Views

irrationality proof of $\sqrt{n}+\sqrt{n+1}$ for any $n>0$

Published on 08 Aug 2016 - 15:59

4.7k

Views

Why aren't all square roots irrational?

Published on 16 Aug 2016 - 0:33

3k

Views

Test of being a rational number for $(1-\frac13+\frac15-\frac17+\cdots)/(1+\frac14+\frac19+\frac1{16}+\cdots)$

Published on 24 Aug 2016 - 17:19

125

Views

Proving that $\log(k)$ is irrational if $k\neq 10^n$

Published on 03 Sep 2016 - 20:39

162

Views

Is $(5+\sqrt[3]2)^n$ ever an integer for $n \in \Bbb Z \setminus \{0\}$?

Published on 11 Sep 2016 - 15:44

452

Views

Is the solution of the equation $ 2\arctan(x) = x $ a rational multiple of $\pi$?

Published on 17 Sep 2016 - 10:53

329

Views

Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?

Published on 25 Sep 2016 - 20:24

2.3k

Views

Solutions to $x^2 = x + 1$ are irrational

Published on 25 Mar 2026 - 20:25

1.5k

Views

Irrationality of $\sqrt{24}$

Published on 02 Oct 2016 - 2:46

309

Views

Is this proposition "$\sqrt2$ + $\sqrt3$ is an irrational number." true or false?

Published on 02 Oct 2016 - 12:56

4.5k

Views

$\sqrt{2}$ is irrational proof using well-Ordering Property

Published on 12 Oct 2016 - 11:11

441

Views

P-adic sequence with a limit outside rational numbers

Published on 22 Oct 2016 - 14:07

List Question

Prove that $\sqrt {2^n-1}$ is irrational for every integer $ n>1$

A simple proof for non-rationality of number $\sqrt[n]{1+q^n}$

Shorter proof of irrationality of $\sqrt{2}$?

irrationality proof of $\sqrt{n}+\sqrt{n+1}$ for any $n>0$

Why aren't all square roots irrational?

Test of being a rational number for $(1-\frac13+\frac15-\frac17+\cdots)/(1+\frac14+\frac19+\frac1{16}+\cdots)$

Proving that $\log(k)$ is irrational if $k\neq 10^n$

Is $(5+\sqrt[3]2)^n$ ever an integer for $n \in \Bbb Z \setminus \{0\}$?

Is the solution of the equation $ 2\arctan(x) = x $ a rational multiple of $\pi$?

Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?

Solutions to $x^2 = x + 1$ are irrational

Irrationality of $\sqrt{24}$

Is this proposition "$\sqrt2$ + $\sqrt3$ is an irrational number." true or false?

$\sqrt{2}$ is irrational proof using well-Ordering Property

P-adic sequence with a limit outside rational numbers

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