Prove that $n^{1/k}$ is irrational unless $n$ is itself an integer $k$th power
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
104548
Geometric proof for irrationality of $\pi$
67605
Different proof that $\sqrt{2}$ is irrational
31331
$|a|=m,\,\gcd(m,n)=1 \implies a$ is an $n$'th power
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
77129
Density of irrationals
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
62996
A problem regarding the proof of ${p^nk\choose p^n}\equiv k\mod p$, where $p\nmid k$.
120906
Is there a proof that $\pi \times e$ is irrational?
67031
use contradiction to prove that the square root of $p$ is irrational
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
4381
Proof that the set of irrational numbers is dense in reals
30523
A binary irrational with bits defined by primes
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
15110
About irrational logarithms
71639
Proof $(1+1/n)^n$ is an increasing sequence
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property