The full wave approach developed earlier to evaluate the radiation fields scattered by deterministic two dimensionally rough surfaces is used here to determine the scattering cross sections for random rough surfaces. The medium below the irregular boundary is characterized by complex permittivity and permeability. For slightly rough surfaces, the full wave solutions for the incoherent scattered fields are shown to be in agreement with the perturbation solution. However, when the major contributions to the scattered fields come from the region of the rough surface around the stationary phase (specular) points, the full wave solutions are in agreement with the physical optics solutions. Thus the full wave solutions which reduce to the perturbation, the physical optics, and the geometrical optics approximations in special cases precisely determine the limitations of these approximations and reconcile the differences between them. The full wave solutions satisfy duality, reciprocity, and realizability relations in electromagnetic theory, and they are invariant under coordinate transformations.