Geometric Mean in terms of Geometry

Let ‘a’ and ‘b’ be two numbers, then the Geometric Mean of two numbers, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b.
Similarly, the Geometric Mean of three numbers, a, b and c is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers.