Is it true that the nth root of a rational number a/b, lowest terms, is rational iff a^(1/n) and b^(1/n) are integers?
10008
Proof that the nth root of a rational s/t is irrational unless s and t are perfect nth powers
22800
Can $\sqrt{n} + \sqrt{m}$ be rational if neither $n,m$ are perfect squares?
107089
finding rational roots of polynomials
69067
Principal $n$th root of a complex number
66272
Is there a common notion of $\mathbb{R}^n$, for non-integer $n$?
80304
Roots of $\,ax^2+bx+c\,$ are irrational if $a,b,c$ are odd integers
109304
The roots of the equation $z^n=(1+z)^n$...
85383
No. Of real roots of an equation
11664
If $a_0+\frac{a_1}{2}+\dots + \frac{a_n}{n+1}=0$ then $a_nx^n+\dots + a_0$ has a root in $[0,1]$
44600
How can I prove: if $p $ is prime and $n>1$, then $ p^{\frac1n} $ is irrational?
81957
How many roots have a complex number with irrational exponent?
103328
Rational Roots of Riemann's $\zeta$ Function
81778
If $m|n$ and $a$ is a primitive root of $n$, show that $a$ is a primitive root of $m$ (understanding a tip)
56802
Why $\sqrt[3]{{2 + \sqrt 5 }} + \sqrt[3]{{2 - \sqrt 5 }}$ is a rational number?
29780
If $x$ is a positive rational but not an integer, is $x^x$ irrational?
16559
Difference between $\mathbb{Z}/n\mathbb{Z}$ and $\mathbb{Z}_n$
37529
If $\sqrt[3]{a} + \sqrt[3]{b}$ is rational then prove $\sqrt[3]{a}$ and $\sqrt[3]{b}$ are rational