In this work, the effect of incompressibility modulus K NM and symmetry energy density J on charge distribution and root-mean-square radii of neutron R n and proton R p has been investigated for light, medium and heavy closed-shell nuclei 40 20 Ca 20 , 48 20 Ca 28 , 90 40 Zr 50 , 116 50 Sn 66 , 144 62 Sm 82 and 208 62 Pb 126 within the framework of self-consistent Hartree-Fock (HF) with 20 types of Skyrme interactions having wide range of nuclear properties such as incompressibility modulus K NM and symmetry energy density J.The nuclear charge densities have been obtained and compared with the experiment data to give us a picture about the internal structure of the investigated nuclei. Also, the relation between the proton and neutron root-mean-square radii, and nuclear matter properties has been studied and examined by determining and discussion the statistical Pearson linear correlation coefficient, to help in formulating nuclear interaction.