If $r+\frac{1}{r}$ is an odd integer then $r$ is irrational
62792
Can sum of a rational number and its reciprocal be an integer?
55077
prove that $2\sqrt5 +\sqrt{11}$ is irrational
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
138446
Proving that there exists an irrational number in between any given real numbers
80304
Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers
147363
Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
126199
Proof of $\pi$ not being a quadratic irrational number.
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
22408
Jutifying: irrational + rational = irrational
30523
A binary irrational with bits defined by primes
92226
Prove $\sqrt6$ is irrational
28347
Prove that $\sqrt 2 + \sqrt 3$ is irrational
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
104548
Geometric proof for irrationality of $\pi$
101162
Square root of $2$ is irrational
118374
Is there a proof that $\pi$ is an irrational number?