how is GM=gR^2?

• When an object is dropped from a height, it falls towards the earth. Thus, the acceleration produced in an object due to the force of gravity is known as acceleration due to gravity (g).

• Acceleration due to gravity at the surface of earth

M − Mass of earth

m − Mass of body lying above the surface of earth

R − Radius of earth

According to Newton’s law of gravitation, the force of attraction between the body and the earth is

 … (i)

However, the force with which a body is attracted towards the earth gives the weight of the body.

∴ F = mg … (ii)

Equating (i) and (ii),

I'd suggest you to go through the study material well. It has been explained well there.