Squares in Algebraic Extensions

Question

Sorry if that's a hard question, but is there an "easy" way to determine when an element inside a (real) simple field extension of $\mathbb Q$, is a perfect square ? (The one in question is a 3rd degree non-integral extension, and the elements have $\mathbb Z$-coefficients, maybe that helps a little). I'm not interested that much in calculating the square root effectively, if it exists inside the extension, though that would help.