How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
32
Is $n^{th}$ root of $2$ an irrational number?
30523
A binary irrational with bits defined by primes
66210
Prove that $z^n + 1/{z^n}$ is a rational number
15110
About irrational logarithms
92226
Prove $\sqrt6$ is irrational
18360
Proof that the irrational numbers are uncountable
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
36546
For an irrational number $a$ the fractional part of $na$ for $n\in\mathbb N$ is dense in $[0,1]$
104548
Geometric proof for irrationality of $\pi$
141424
$\log_7 n$ is either an integer or an irrational number
53945
The square root of a prime number is irrational
32848
Prove that the product of a non-zero rational and irrational number is irrational.
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
109953
How to prove that $\sqrt 3$ is an irrational number?
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
69264
Is there an irrational number $a$ such that $a^a$ is rational?