Irrationality of $\sqrt{3}$
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
124641
Prove that $5^{1/3}+7^{1/2}$ is irrational
125267
Prove that $2^{1/2}$ is irrational
118374
Is there a proof that $\pi$ is an irrational number?
115834
Cubic polynomial with three (distinct) irrational roots
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
104548
Geometric proof for irrationality of $\pi$
69264
Is there an irrational number $a$ such that $a^a$ is rational?
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
1877
Can an irrational number raised to an irrational power be rational?
64885
Irrational and rational sequence proof
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
129521
Is $\sqrt[3]{5}$ in $\mathbb Q(\sqrt[3]{2})$?
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$