Why aren't all square roots irrational?
2926
The contradiction method used to prove that the square root of a prime is irrational
31327
Why is $\sqrt{x}$ a function?
39170
Existence of square root
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
96204
Irrational number $\sqrt2$ proof
81428
Why does proof by contradiction not work on Rational numbers but only on Irrational numbers?
125812
Is sin(x) necessarily irrational where x is rational?
22408
Jutifying: irrational + rational = irrational
126199
Proof of $\pi$ not being a quadratic irrational number.
53958
General misconception about $\sqrt x$
48035
Prove that square root of 2 is irrational using the principle of Mathematical Induction
22762
How can adding an infinite number of rationals yield an irrational number?
147777
If $P$ and $Q$ are distinct primes, how to prove that $\sqrt{PQ}$ is irrational?
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
127830
proof that $\sqrt(2)$ is irrational / why is the fraction irreducible
69264
Is there an irrational number $a$ such that $a^a$ is rational?
19676
Is it known whether ${\sqrt{2}}^{\sqrt{2}}$ is irrational?