Proof about square roots of rational numbers being rational/irrational
98496
Let $a,b \in \mathbb{Q^{+}}$ then $\sqrt{a} + \sqrt{b} \in \mathbb{Q} $ iff $\sqrt{a} \in \mathbb{Q}$ and $\sqrt{b} \in \mathbb{Q}$
7500
$\arctan$ of a square root as a rational multiple of $\pi$
68456
Prove that there exists irrational numbers $x$ and $y$ such that $x + y$ is rational, without using subtraction
138446
Proving that there exists an irrational number in between any given real numbers
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
92226
Prove $\sqrt6$ is irrational
144244
Bound on difference between irrational square root and rational number
87735
Prove that the roots $\in \Bbb R$ of $x^3+x+1=0$ aren't rational without RRT
96204
Irrational number $\sqrt2$ proof
124641
Prove that $5^{1/3}+7^{1/2}$ is irrational
86882
Proving Gauss' polynomial theorem (Rational Root Test)
53945
The square root of a prime number is irrational
58284
How to prove that $\sqrt[3] 2 + \sqrt[3] 4$ is irrational?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
109953
How to prove that $\sqrt 3$ is an irrational number?
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
89716
Is there a proof of the irrationality of $\sqrt{2}$ that involves modular arithmetic?