Use dimensions to check that GM/R² is an acceleration.

Step 1. (a). $\dfrac{[\text{M}^{-1}\,\text{L}^{3}\,\text{T}^{-2}][\text{M}]}{[\text{L}^{2}]} = [\text{L}\,\text{T}^{-2}]$: an acceleration, as it must be.

Step 2. (b). $M = \dfrac{gR^2}{G} = \dfrac{1.62 \times (1.737 \times 10^{6})^2}{6.67 \times 10^{-11}} = \dfrac{4.888 \times 10^{12}}{6.67 \times 10^{-11}} = 7.33 \times 10^{22}\ \text{kg}$.