Show that $\sqrt n$ is irrational if $n$ is not a perfect square, using the method of infinite descent.
67605
Different proof that $\sqrt{2}$ is irrational
30622
Proving $\sqrt 3$ is irrational.
88429
Prove $\sqrt{2} + \sqrt{5}$ is irrational
157847
If $x_n \to 0$, show that $\sqrt{x_n} \to 0$
11069
Deciding whether $2^{\sqrt2}$ is irrational/transcendental
158066
Prove $2^{1/3}$ is irrational.
132115
Verify my proof of the irrationality of $\sqrt{6}$.
34710
Cardinality of Irrational Numbers
106716
The sum of square roots of non-perfect squares is never integer
6275
How can you prove that the square root of two is irrational?
122226
Incorrect logic in popular proof of the irrationality of $\sqrt2$?
158730
Is $\ln(\ln(n))$ irrational for any integer $n>1$?
48975
Transcendental numbers and irrationality measure
72144
Show that $\mathbb Q(\sqrt p) \not\simeq\mathbb Q(\sqrt q)$
31744
Proving that there is an irrational number between any two unequal rational numbers.
49750
Proof of the square root inequality $2\sqrt{n+1}-2\sqrt{n}<\frac{1}{\sqrt{n}}<2\sqrt{n}-2\sqrt{n-1}$
39021
Proving that $\sqrt{2}+\sqrt{3}$ is irrational