List questions from rationality-testing | MathQa

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

Published on 12 Jan 2025 - 23:58

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

Published on 12 Jan 2025 - 18:44

Adding or Multiplying Transcendentals

Published on 12 Jan 2025 - 9:09

Can a pre-calculus student prove this?

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09

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

Published on 12 Jan 2025 - 9:09