Answer
Yes, I agree that my classmate's statement is true by looking at the way we find the geometric mean of two numbers.
Work Step by Step
Let's look at the way we find the geometric mean of two numbers.
The geometric mean of two numbers can be found using the following proportion:
$\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are positive numbers and $x$ is the geometric mean.
Use the cross products property to get rid of the fractions:
$x^2 = ab$
Take the square root of both sides to simplify:
$x = \sqrt {ab}$
Yes, I agree that my classmate's statement is true.
