Particularly in Sr2IrO4, the interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion stabilizes a J(eff) = 1/2 spin-orbital entangled insulating state at low temperatures. Whether this insulating phase is Mott- or Slater-type, has been under intense debate. We address this issue via spatially resolved imaging and spectroscopic studies of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy (STM/S). STS results clearly illustrate the opening of an insulating gap (150 ~ 250 meV) below the Néel temperature (TN), in qualitative agreement with our density-functional theory (DFT) calculations. More importantly, the temperature dependence of the gap is qualitatively consistent with our DFT + dynamical mean field theory (DMFT) results, both showing a continuous transition from a gapped insulating ground state to a non-gap phase as temperatures approach TN. These results indicate a significant Slater character of gap formation, thus suggesting that Sr2IrO4 is a uniquely correlated system, where Slater and Mott-Hubbard-type behaviors coexist.