List questions from rationality-testing

Published on 06 Oct 2015 - 15:58

322

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rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$

Published on 08 Oct 2015 - 7:05

122

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Prove that there are no integers $x$ and $y$ such that $ (x/y)^2 = 2$

Published on 08 Oct 2015 - 16:49

729

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Proof that $2\sqrt2 + \sqrt7$ is an irrational number

Published on 20 Mar 2026 - 22:33

328

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Proving $\sqrt[4]{4}$ is irrational

Published on 19 Oct 2015 - 18:28

641

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Adding or Multiplying Transcendentals

Published on 02 Mar 2026 - 6:22

3.4k

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Can a pre-calculus student prove this?

Published on 24 Mar 2026 - 2:07

1.1k

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Prove that between any two rational numbers, there are two irrational numbers whose difference is rational

Published on 07 Mar 2026 - 21:43

1k

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Prove that the product of an irrational number and a rational number is irrational.

Published on 26 Feb 2026 - 19:31

247

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Are there numbers $x, y \in \mathbb{Q}$ such that $\tan(x) + \tan(y) \in \mathbb{Q}$?

Published on 04 Nov 2015 - 18:02

77

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Can we construct three irrational numbers $a,b,c$ such that $a+b+c \in \mathbb Q$?

Published on 20 Nov 2015 - 16:17

112

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When are both $x$ and $ y$ rational in $ x^2 + y^2 = k$

Published on 23 Nov 2015 - 6:43

364

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Is $a\sqrt[3]{2} + b\sqrt[3]{4}$ irrational?

Published on 28 Feb 2026 - 3:01

400

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Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational

Published on 23 Nov 2015 - 18:51

245

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Is $\sum_{p}\frac{1}{p^{2}}$ irrational?

Published on 10 Dec 2015 - 18:29

List Question

Prove $\log_{12}18$ is irrational

rational number solutions to $\frac{a}{a^2+1} + \frac{b}{b^2+1} = \frac{c}{c^2+1}$ with $abc\ne 0$

Prove that there are no integers $x$ and $y$ such that $ (x/y)^2 = 2$

Proof that $2\sqrt2 + \sqrt7$ is an irrational number

Proving $\sqrt[4]{4}$ is irrational

Adding or Multiplying Transcendentals

Can a pre-calculus student prove this?

Prove that between any two rational numbers, there are two irrational numbers whose difference is rational

Prove that the product of an irrational number and a rational number is irrational.

Are there numbers $x, y \in \mathbb{Q}$ such that $\tan(x) + \tan(y) \in \mathbb{Q}$?

Can we construct three irrational numbers $a,b,c$ such that $a+b+c \in \mathbb Q$?

When are both $x$ and $ y$ rational in $ x^2 + y^2 = k$

Is $a\sqrt[3]{2} + b\sqrt[3]{4}$ irrational?

Prove that $\sqrt{10} - \sqrt6 - \sqrt5 + \sqrt3$ is irrational

Is $\sum_{p}\frac{1}{p^{2}}$ irrational?

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