Proving that $\sqrt{3} +\sqrt{7}$ is rational/irrational
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
69631
Prove that: $ \cot7\frac12 ^\circ = \sqrt2 + \sqrt3 + \sqrt4 + \sqrt6$
158066
Prove $2^{1/3}$ is irrational.
138446
Proving that there exists an irrational number in between any given real numbers
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
124641
Prove that $5^{1/3}+7^{1/2}$ is irrational
31744
Proving that there is an irrational number between any two unequal rational numbers.
67605
Different proof that $\sqrt{2}$ is irrational
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
156766
Prove that $\sqrt{\frac{n}{n+1}}\notin \mathbb{Q}$
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
67031
use contradiction to prove that the square root of $p$ is irrational
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
44307
Prove $\sqrt[3]{3} \notin \mathbb{Q}(\sqrt[3]{2})$
115834
Cubic polynomial with three (distinct) irrational roots
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?