[math-fun] 12th degree radicals?

In http://mathworld.wolfram.com/SquareDissection.html, x₂ satisfies 6 - 4 √2 + (-24 + 16 √2) x + (28 - 20 √2) x^2 + (-8 + 8 √2) x^3 - 2 x^4 + x^6, whereat my sextic solver chokes on the √2s. Does anybody know if x comes out in radicals? --rwg