How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
111094
Help with proving that $\pi$ is irrational
56802
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
28218
Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
23752
Proving Irrationality
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
64885
Irrational and rational sequence proof
87682
Show that $\sqrt{2}\notin \mathbb{Q}(\sqrt[4]{3})$
34906
Showing $[\mathbb{Q}(\sqrt[4]{2},\sqrt{3}):\mathbb{Q}]=8$.
40009
Show that $e^{\sqrt 2}$ is irrational
17930
Please explain this step in proving the square root of 3 is irrational
143733
Is this proof that $\sqrt 2$ is irrational correct?
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
109175
Why is it hard to prove whether $\pi+e$ is an irrational number?