If $\sqrt{n}$ is not an integer, are there any rational numbers $x$ such that $x^2 = n$?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
6275
How can you prove that the square root of two is irrational?
91101
Proving $\sqrt2$ is irrational
20486
Numbers representable as $x^2 + 2y^2$
20619
Finding Rational numbers
109305
Non-existence of natural numbers such that $\sqrt{n} +\sqrt{n+1} <\sqrt{x} +\sqrt{y} <\sqrt{4n+2}$
109953
How to prove that $\sqrt 3$ is an irrational number?
69264
Is there an irrational number $a$ such that $a^a$ is rational?
31436
Show that for all $a\in\mathbb{N}$, there exists $b\in\mathbb{N}$ and square-free integer $c$ such that $\sqrt{a}=b\sqrt{c}$.
144244
Bound on difference between irrational square root and rational number
69874
Are there any integer solutions to $a^3=b^2$?
53945
The square root of a prime number is irrational
24301
Can a finite sum of square roots be an integer?
53331
$\mathbb{Q}(\sqrt2, \sqrt3)$ is not isomorphic to $\mathbb{Q}(\sqrt[4]2)$
40009
Show that $e^{\sqrt 2}$ is irrational
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
43470
Prove: For odd integers $a$ and $b$, the equation $x^2 + 2 a x + 2 b = 0$ has no integer or rational roots.