Absolute Magnitude of the Full Moon

[Fabio010]

Hey guys, I was doing some homework and found something I don't quite understand. When calculating the absolute magnitude of the Full Moon, I came across a square root of its Albedo.

(here - http://space.wikia.com/wiki/Absolute_magnitude). No idea why it's squared, but I can't get the +0,25 any other way so I guess it's there to stay?b]

 

[mfb]

The square root is used to get the log scale right:
As an example: A factor of 100 in the albedo corresponds to a factor of 100 in the light intensity, which is a difference of 5 in the apparent magnitude and therefore a difference of 1 in the logarithm, which corresponds to a factor of 10 in the argument of the logarithm. Therefore, you need the square root of the albedo in that formula.

Take the log with base 100 (or 2.5*log instead of 5*log), and you can use $\frac{ar^2}{d^2}$ as argument, which directly corresponds to the intensity.