Proof that $\sqrt[p]{n}$ is irrational if $n$ is not a perfect pth power
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
30478
How to prove that a number is irrational
18360
Proof that the irrational numbers are uncountable
92226
Prove $\sqrt6$ is irrational
125267
Prove that $2^{1/2}$ is irrational
106716
The sum of square roots of non-perfect squares is never integer
131634
Prove the irrationality of $0.235711131719...$
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
143733
Is this proof that $\sqrt 2$ is irrational correct?
48975
Transcendental numbers and irrationality measure
42292
Show that $a_n<\sqrt{2}$ for every $n\in\mathbb{N}$.
43048
When is $2^n \pm 1$ a perfect power
17930
Please explain this step in proving the square root of 3 is irrational