Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
70315
Process to show that $\sqrt 2+\sqrt[3] 3$ is irrational
109953
How to prove that $\sqrt 3$ is an irrational number?
43300
The degree of $\sqrt{2} + \sqrt[3]{5}$ over $\mathbb Q$
18360
Proof that the irrational numbers are uncountable
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
56464
Proving the irrationality of $e^n$
37915
$\sqrt{2}$ is irrational proof using well-Ordering Property
21826
How to prove $\sqrt{5+\sqrt{5+\sqrt{5-\sqrt{5+\sqrt{5+\sqrt{5+\sqrt{5-\cdots}}}}}}} = \frac{2+\sqrt 5 +\sqrt{15-6\sqrt 5}}{2}$
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
5529
Proving that $x$ is irrational if $x-\lfloor x \rfloor + \frac1x - \left\lfloor \frac1x \right\rfloor = 1$
134885
proving that $\mathbb{Q}(\sqrt{5}, \sqrt{6}) = \mathbb{Q}(\sqrt{5}+ \sqrt{6}) $
43985
Why must $a$ and $b$ both be coprime when proving that the square root of two is irrational?
115834
Cubic polynomial with three (distinct) irrational roots