Proof that $\sqrt6 - \sqrt2 - \sqrt3$ is irrational.
129433
$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$ is Irrational
99311
Prove $2^{1/3} + 2^{2/3}$ is irrational
31744
Proving that there is an irrational number between any two unequal rational numbers.
56464
Proving the irrationality of $e^n$
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
138446
Proving that there exists an irrational number in between any given real numbers
67605
Different proof that $\sqrt{2}$ is irrational
40009
Show that $e^{\sqrt 2}$ is irrational
158933
Rational solutions of $y^2 = x^3 - x$
142000
Prove that there is an irrational number and a rational number between any two distinct real numbers
138501
Is $\mathbf{Q}(\sqrt{2},\sqrt{3}) = \mathbf{Q}(\sqrt{6})$?
69575
If $ad$ and $bc$ are odd and even, respectively, then prove that $ax^3+bx^2+cx+d$ has an irrational root.
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
75639
Showing that $\sqrt[3]{2}\notin\Bbb Q(\alpha_1,...,\alpha_k)$ where $\alpha_i^2\in\Bbb Q\ \forall i$
59391
$p,q,r$ primes, $\sqrt{p}+\sqrt{q}+\sqrt{r}$ is irrational.
125267
Prove that $2^{1/2}$ is irrational
103496
Show that $3p^2=q^2$ implies $3|p$ and $3|q$