  Real Space Renormalization Group (RSRG) treatment of Ising model for square
and simple cubic lattice is investigated and critical coupling strengths of
these lattices are obtained. The mathematical complications, which appear
inevitable in the decimated partition function due to Block-spin
transformation, is treated with a relevant approximation. The approximation is
based on the approximate equivalence of $\ln(1+f(K,\{\sigma_{n.n}\})) \simeq
f(K,\{\sigma_{n.n}\})$ for small $f(K,\{\sigma_{n.n}\})$, here $K$ is the
nearest neighbor coupling strength and $\{\sigma_{n.n}\}$ is the nearest
neighbor spins degrees of freedom around a central spin. The values of the
critical coupling strengths are obtained as $0.4830$ for square lattice and
$0.2225$ for simple cubic (SC) lattice. The corresponding critical exponents
values $\alpha$ and $\nu$ are also calculated within very acceptable agreement
with those values obtained from numerical works.
