Prove $\sqrt{k}$ is not a rational number.
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
11710
How to show that $\mathbb{Q}$ is not $G_\delta$
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
143733
Is this proof that $\sqrt 2$ is irrational correct?
33628
Prove that $\sin(\sqrt x)$ not periodic
18484
Show that $k[x,y,z]/(xz-y^2)$ is not a UFD.
23752
Proving Irrationality
8589
$\sqrt[b_1]{a_1}+\sqrt[b_2]{a_2}+\cdots+\sqrt[b_k]{a_k}$ not an integer
127605
What are some methods to show $\log$ is not a rational function?
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
69046
Proof of $\mathbb{Q}$ is not cyclic
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
32848
Prove that the product of a non-zero rational and irrational number is irrational.
39114
Prove that a set in $\mathbb R^3$ is not an algebraic set