3.8 Geometric Mean Practice

The geometric mean is defined as $$\text{Geometric Mean} = \text{sqrt}(a \times b)$$ .

Take the square root of both sides: $$x = \text{sqrt}(36) = 6$$ or $$x = -6$$ .

The geometric mean of n numbers is given by $$\text{Geometric Mean} = \text{n-th root}(x_1 \times x_2 \times ... \times x_n)$$ .

Possible pairs include (4, 9) since $$\text{sqrt}(4 \times 9) = 6$$ .

$$z = \text{sqrt}(117) = 3\text{sqrt}(13)$$ .

The arithmetic mean is always greater than or equal to the geometric mean for non-negative numbers.

$$z = \text{sqrt}(396) = 6\text{sqrt}(11)$$ .

$$\text{Geometric Mean} = \text{sqrt}(2 \times 8) = \text{sqrt}(16) = 4$$ .

$$x = \text{sqrt}(20) = 2\text{sqrt}(5)$$ .

$$\text{Geometric Mean} = \text{sqrt}(1 \times 25) = \text{sqrt}(25) = 5$$ .