Find the degree of a field extension and proving polynomial irreducible

Question

I'm looking for the degree $|\mathbb{Q}(\sqrt{3+2\sqrt2}): \mathbb{Q}|$ and I found that $\sqrt{3+2\sqrt2}$ is a root of $f(x) = x^4-6x^2+1$ but I have trouble proving that this polynomial is irreducible. (tried the substitution trick but doesn't work, eisenstein doesn't work either)

Answer 1

It's reducible: $$ x^4-6x^2+1= (x^2 - 2 x - 1) (x^2 + 2 x - 1) $$