What exactly are those "two irrational numbers" $x$ and $y$ such that $x^y$ is rational?
1877
Can an irrational number raised to an irrational power be rational?
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
87410
Are there real numbers that are neither rational nor irrational?
34825
Intuitive explanation for how could there be "more" irrational numbers than rational?
41767
Sequence of rational numbers converging to an arbitrary irrational number $\beta$.
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
22408
Jutifying: irrational + rational = irrational
13572
$x^y+y^x>1$ for all $(x, y)\in \mathbb{R_+^2}$
42444
Irrationality of $\sum_{p\in\mathbb{P}} \frac{1}{2^{p}}$
100319
Functional equation with strange property about irrational numbers
125812
Is sin(x) necessarily irrational where x is rational?
64885
Irrational and rational sequence proof
150576
When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
138446
Proving that there exists an irrational number in between any given real numbers