How can I prove $\sqrt{2} ^{\sqrt{2}}$ is irrational?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
18360
Proof that the irrational numbers are uncountable
67605
Different proof that $\sqrt{2}$ is irrational
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
120906
Is there a proof that $\pi \times e$ is irrational?
55582
How can I show that $\sqrt{1+\sqrt{2+\sqrt{3+\sqrt\ldots}}}$ exists?
32
Is $n^{th}$ root of $2$ an irrational number?
15110
About irrational logarithms
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
21237
$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational
151439
$\sqrt{1-x^2}$ is not a rational function
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
12020
Prove $\sqrt{n+1}-\sqrt{n}\lt \frac{1}{2\sqrt{n}}$