can any one tell me what is the difference between the (F2-F

can any one tell me what is the difference between the (F2-F1)/2 and the (√F1*√F2) formula used to determine the center frequency?

In filter design it is practice to use (√F1*√F2) to find the center of frequency for the filter.
(F2-F1)/2 will give the half band width