# Geometric Mean Illustration

Definition: The GEOMETRIC MEAN of two numbers a and b is defined to be the square root of their product. That is, the GEOMETRIC MEAN of a and b = . In the applet below, the purple segment that will soon appear is the GEOMETRIC MEAN of a and b. Interact with the applet for a few minutes. Be sure to change the lengths of a and b as you do. Then, answer the questions that follow.

## 1.

What is the geometric mean of 5 and 20?

## 2.

What is the geometric mean of 4 and 5?

## 3.

12 is the geometric mean of 36 and what other number?

## 4.

Prove that the purple segment drawn in the semicircle above has a length equal to the geometric mean of a and b.