Simplifying the Equation for Beginners

[LENIN]

I have to find out how to make this simplification
2\pi \sqrt{ \frac {Ml^2+2Mr^2/5+m(l-r)^2/3} {(Ml+m(l-r)/2)g}} \approx 2\pi \sqrt{\frac{l}{g}(1+\frac{2r}{5l}-\frac{1m}{6M})}.

This is for a project I have to do, but I have never done any such simplifications before. I don't know which parts of the equation are important and which aren't. If it helps this are the values of the variables:

M\approx10kg
m\approx20g
l=227cm
r=6cm

 

[Astronuc]

(Ml+m(l-r)/2)g would simplify to ~Mlg, in the denominator under the root.

(l-r)² would simplify to l² for very small r, otherwise l²-2rl since r² would be small.

r/l = 6/227 = 0.026

m/M = 0.02/10 = 0.002 so M-m ~ M is a good approximation.

 

[LENIN]

Thank you.