There are no rationals $r, s$ such that $\sqrt{3} = r + s\sqrt{2}$.
140063
An element not in a field extension
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?
39346
Let $R= \mathbb{Q}[x^2 ,x^3 ]$, the set of all polynomials over $\mathbb{Q}$ with no $x$ term. Show that the $\gcd$ of $x^5$ and $x^6$ does not exist
30622
Proving $\sqrt 3$ is irrational.
44440
Prove $\sqrt{2}+\sqrt[3]{5}$ is irrational
67161
No maximum(minimum) of rationals whose square is lesser(greater) than $2$.
51649
prove there is no smallest positive rational number
18360
Proof that the irrational numbers are uncountable
67031
use contradiction to prove that the square root of $p$ is irrational
106242
Why no common factors in proving root 2 is irrational?
138193
Why is $\sqrt {12} = 2 \sqrt 3$?
147534
The set of irrational numbers is not a $F_{\sigma}$ set.
68315
Why doesn't multiplying square roots of imaginary numbers follow $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$?
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
56877
Show that $\sqrt{4 + 2\sqrt{3}} - \sqrt{3}$ is rational.
4946
Non-existence of irrational numbers?
74229
$2x^2+3y^2=z^2$ does not have a non-zero integral solution.