Find the monic quartic polynomial f(x) with rational coefficients whose roots include x = 2 - sqrt(2) and x = 3 + sqrt(6).
This will be \(f(x) = (x-2-\sqrt2)(x-2+\sqrt2)(x-3-\sqrt6)(x-3+\sqrt6)\)
I'll leave you to multiply it out to confirm that it does indeed have rational coefficients.
Edit: corrected signs. Thanks to EP for making me aware of this.