geometric mean

The geometric mean of two numbers a and b can be interpreted as the length of a side of a square having the same area as a rectangle with a and b as its sides.

So the rectangle having 4 and 16 as its sides has an area of 64

And a square with area 64 will have a side =  to the square root of this, i.e., 8.

So.....8  is the geometric mean of 4 and 16

Sqrt(4×16)=2×4=8

The geometric of the numbers a and b is the number x that solves this equation:  a/x  =  x/b.

Another way to write this is:  x²  =  a·b  or  x =  ±√(a·b).

x  =  ±√(4·16)  =  ±√(64)  =  ±8