If you are doing complex algebra you should already be aware of De'Moivre's theorem. For z=(x+jy) then:
z=Re^jθ = R(Cosθ+jSinθ)
with x=RCosθ, y=RSinθ, R=√(x^2+y^2), θ=ArcTan(y/x) and
z^n=R^n .e^jnθ
which holds for integer or fractional n e.g in your case ½. You should now be able to find the rationalized expression you want.