How to prove that $\sqrt{2} + \sqrt{7}$ is irrational?
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
126074
Proof of the irrationality of $\sqrt{3}$ - logic question
92226
Prove $\sqrt6$ is irrational
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
84558
Prove that the square root of a positive integer is either an integer or irrational
7491
How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?
20315
$\sqrt[31]{12} +\sqrt[12]{31}$ is irrational
120906
Is there a proof that $\pi \times e$ is irrational?
2926
The contradiction method used to prove that the square root of a prime is irrational
150576
When is an Integer a Rational Number, and are All Ratios Rational, Even $\frac{\sqrt{7}}{2}$?
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational
111094
Help with proving that $\pi$ is irrational
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
96204
Irrational number $\sqrt2$ proof
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
87596
Is $\sum_{p}\frac{1}{p^{2}}$ irrational?
78287
Prove that if $n$ is not the square of a natural number, then $\sqrt{n}$ is irrational.