B2 Geometric Mean Review

The geometric mean of two numbers a and b is defined as the square root of their product: $$\text{Geometric Mean} = \text{GM} = \text{sqrt}(a \times b)$$ .

The geometric mean is $$\text{GM} = \text{sqrt}(64 \times 25) = \text{sqrt}(1600) = 40$$ .

The geometric mean of n numbers x1, x2, ..., xn is given by: $$\text{GM} = \text{sqrt[n]}{x_1 \times x_2 \times ... \times x_n}$$ .

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

The geometric mean is $$\text{GM} = \text{sqrt}(81 \times 4) = \text{sqrt}(324) = 18$$ .

Using the formula: $$\text{GM} = \text{sqrt}(x \times 16) = 8$$ , we find that $$x = 4$$ .

The geometric mean is $$\text{GM} = \text{sqrt}(36 \times 64) = \text{sqrt}(2304) = 48$$ .

Let the other number be y. Then, $$\text{GM} = \text{sqrt}(5 \times y) = 10$$ , leading to $$y = 20$$ .

Using the formula: $$\text{GM} = \text{sqrt}(z \times 30) = 15$$ , we find that $$z = 7.5$$ .

The geometric mean is $$\text{GM} = \text{sqrt}(1 \times 100) = \text{sqrt}(100) = 10$$ .