TITLE: Minimal polynomial of the root of algebraic number
QUESTION [6 upvotes]: I have obtained the minimal polynomial of $9-4\sqrt{2}$ over $\mathbb{Q}$ by algebraic operations:
$$ (x-9)^2-32 = x^2-18x+49.$$
I wonder how to calculate the minimal polynomial of $\sqrt{9-4\sqrt{2}}$ with the help of this sub-result? Or is there a smarter way to do this (not necessarily algorithmic)?

REPLY [2 votes]: Maple can calculate minimal polynomials, e.g.:

evala(Norm(convert(sqrt(9-4*sqrt(2)),RootOf) - z));

$-7+2z+z^2$