THE VALUE OF g AT THE MOON IS 1/6 th OF THE VALUE OF g AT EARTH SURFACE , & THE DIAMETER OF THE MOON

The formula of escape velocity is (2gR)^(1/2), remember ^(1/2) resembles for square root.
Then, the escape velocity of earth is (2gR)^(1/2)

With respect to earth, gravity of moon is (g/6)
diameter is (D/4) and radius is (R/8)

Now, substituting in the formula, we get
escape velocity of moon is (2*g/6*R/8)^(1/2)
= (2gR/48)^(1/2)

Now to find ratio of escape velocity of earth to moon is
(2gR)^(1/2) / (2gR/48)^(1/2)
= 48/1
Hence the ratio is 48:1