Prove irrationality of $\sqrt{2+\sqrt{2}}$ and $\sqrt{2}+\sqrt{3}$
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
30478
How to prove that a number is irrational
111094
Help with proving that $\pi$ is irrational
23752
Proving Irrationality
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
86988
Cardinality of the Irrationals
143733
Is this proof that $\sqrt 2$ is irrational correct?
40348
Proving by mathematical induction: $1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{n}}>2(\sqrt{n+1}-1)$
87111
Prove $\sqrt{2}$ is between $\dfrac{a}{b}$ and $\dfrac{a+2b}{a+b}$
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
101162
Square root of $2$ is irrational
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.