Prove that $\sqrt{2} + \sqrt{n}$ is irrational when $n\in\mathbb{N}$
46831
Show that $ a，b, \sqrt{a}+ \sqrt{b} \in\mathbb Q \implies \sqrt{a},\sqrt{b} \in\mathbb Q $
75204
Irrationality $\sqrt{2}$ with ideal
52157
Prove that $d(n)\leq 2\sqrt{n}$
23752
Proving Irrationality
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
125267
Prove that $2^{1/2}$ is irrational
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
73277
Prove $[\sqrt{x}+\sqrt{x+1}]=[\sqrt{4x+2}], x \in \Bbb N$
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
109953
How to prove that $\sqrt 3$ is an irrational number?
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
40009
Show that $e^{\sqrt 2}$ is irrational
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
15110
About irrational logarithms
67605
Different proof that $\sqrt{2}$ is irrational