n To determine the geometric mean of a number, first the combined product of all the numbers is taken out , then the nth square root of that product is taken. Algebraically a1, a2, ..., an being the geometric average , the geometric average can also be thought of as the antilogue of the logical mathematical average of the numbers. Example: 2 and 8 have a geometric mean , {\ displaystyle GM = {\ sqrt {2 \ cdot 8}} = 4.} ( See wiki).