Proving $\sqrt{2}$ is irrational: why $ q = p - \frac{p^2 -2}{p+2}$
4552
Choice of $q$ in Baby Rudin's Example 1.1
35837
How to prove that any (integer)$^{1/n}$ that isn't an integer, is irrational?
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
32
Is $n^{th}$ root of $2$ an irrational number?
158066
Prove $2^{1/3}$ is irrational.
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational
126199
Proof of $\pi$ not being a quadratic irrational number.
64885
Irrational and rational sequence proof
62485
How can I prove $\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}^{\sqrt{2}...}}}}=2$
37642
Why is $\pi$ irrational if it is represented as $C/D$?
10882
irrationality of $\sqrt{2}^{\sqrt{2}}$.
111094
Help with proving that $\pi$ is irrational
153043
Show that $\sqrt{4+2\sqrt{3}}-\sqrt{3}$ is rational using the rational zeros theorem
143733
Is this proof that $\sqrt 2$ is irrational correct?
139755
Prove that $\sqrt{2}+\sqrt{3}+\sqrt{5}$ is irrational. Generalise this.
106242
Why no common factors in proving root 2 is irrational?