Show that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
110588
Showing $\lim_{n\rightarrow\infty}\sqrt[3]{n^3+n^2}-\sqrt[3]{n^3+1}\rightarrow\frac{1}{3}$
104548
Geometric proof for irrationality of $\pi$
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
84558
Prove that the square root of a positive integer is either an integer or irrational
115834
Cubic polynomial with three (distinct) irrational roots
123295
How does one evaluate $\sqrt[3]{x + iy} + \sqrt[3]{x - iy}$?
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
26109
Show that $\arctan(n)$ is irrational for all $n \in \mathbb{N}$
128387
Given that $a+b\sqrt[3]{2} +c\sqrt[3]{4} =0$, where $a,b,c$ are integers. Show $a=b=c=0$
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
109953
How to prove that $\sqrt 3$ is an irrational number?
127764
Showing that $\mathbb{Q}[\sqrt{2}, \sqrt{3}]$ contains multiplicative inverses
75349
Minimal polynomial of $\sqrt[3]{2} + \sqrt{3}$
126427
Proving $\sqrt{2}+\sqrt[3]{3}$ is algebraic.
32
Is $n^{th}$ root of $2$ an irrational number?
111094
Help with proving that $\pi$ is irrational