prove that if $p$ is a prime number, then $\sqrt{p}$ is an irrational number.
67031
use contradiction to prove that the square root of $p$ is irrational
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
23752
Proving Irrationality
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
84603
Prove that if $p$ is a prime such that $p^2+2$ is a prime then $p=3$.
152172
Does there exist a positive irrational number $\alpha $, such that for any positive integer $n$ the number $\lfloor n\alpha \rfloor$ is not a prime?
56464
Proving the irrationality of $e^n$
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
22742
Prove that if $p$ and $p^2+2$ are prime then $p^3+2$ is prime too
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
120906
Is there a proof that $\pi \times e$ is irrational?
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
91101
Proving $\sqrt2$ is irrational
2926
The contradiction method used to prove that the square root of a prime is irrational