Answer
The geometric mean of $10$ and $15$ is $5 \sqrt 6$.
Work Step by Step
The geometric mean of two numbers is given by the following formula:
$\frac{a}{x} = \frac{x}{b}$, where $a$ and $b$ are positive numbers and $x$ is the geometric mean.
Let's plug in our numbers:
$\frac{10}{x} = \frac{x}{15}$
Use the cross products property to get rid of the fractions:
$x^2 = 150$
Rewrite $150$ as the product of a perfect square and another factor:
$x^2 = 25 • 6$
Take the positive square root to solve for $x$:
$x = 5 \sqrt 6$
