Show that for any positive integer n, the kth root of n is either an integer or irrational
1383
How to prove: if $a,b \in \mathbb N$, then $a^{1/b}$ is an integer or an irrational number?
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
41486
If $x^n + a_{n-1}x^{n-1} + ... + a_0 = 0$ has a rational root, then such root is an integer
124641
Prove that $5^{1/3}+7^{1/2}$ is irrational
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
16660
Prove that any positive number has an $n$th root
98440
Show that any non-negative rational integer may be written as the sum of two squares if it is of the form....
32
Is $n^{th}$ root of $2$ an irrational number?
108429
Show that if $x_n \to x$ then $\sqrt{x_n} \to \sqrt{x}$
158730
Is $\ln(\ln(n))$ irrational for any integer $n>1$?
11069
Deciding whether $2^{\sqrt2}$ is irrational/transcendental
21237
$\sqrt{6}-\sqrt{2}-\sqrt{3}$ is irrational
80304
Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers
67605
Different proof that $\sqrt{2}$ is irrational
149549
Infimum of $n$-th root of $n$
43940
Showing that $n$ is pseudoprime to the base $a$
30523
A binary irrational with bits defined by primes