Proof that we can find rational numbers arbitrarily close to $\sqrt{2}$: direct approach.
24706
Is there a rational number between any two irrationals?
7500
$\arctan$ of a square root as a rational multiple of $\pi$
155112
Are there more rational numbers than integers?
88425
Prove that $\,\sqrt [n] n < 1 + \sqrt{\frac{2}{n}}\,$
30622
Proving $\sqrt 3$ is irrational.
92226
Prove $\sqrt6$ is irrational
140841
Induction proof of lower bound for $\sum \sqrt n$
132115
Verify my proof of the irrationality of $\sqrt{6}$.
104841
Can $\sin n$ get arbitrarily close to $1$ for $n\in\mathbb{N}?$
140949
Proving that for each prime number $p$, the number $\sqrt{p}$ is irrational
150037
Finding the simplest rational in a closed interval
143733
Is this proof that $\sqrt 2$ is irrational correct?
114442
Completion of rational numbers via Cauchy sequences
34825
Intuitive explanation for how could there be "more" irrational numbers than rational?
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
138446
Proving that there exists an irrational number in between any given real numbers
1190
Square Root of Rational Number $\frac{A}{B}$