All roots are algebraic numbers, trivially:

n√r = x
r = x^n
x^n - r = 0

Given n and r are constants, that's a polynomial! The root of it is thus an algebraic number.

But there are roots of polynomials that aren't expressable with square roots, cube roots, or any other roots!

So does anyone know what the subset of the Algebraic Numbers that are the Field Extension of rational numbers with the operation of roots is called?

If it's exclusively Square Roots, that's "Constructible Numbers", but what about any roots, not just square?

#Math
#NumberTheory