## Geometry: Common Core (15th Edition)

$3 \sqrt 7$
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. Let's plug in our numbers: $\frac{7}{x} = \frac{x}{9}$ Use the cross products property to get rid of the fractions: $x^2 = 63$ Rewrite $63$ as the product of a perfect square and another factor: $x^2 = 9 • 7$ Take the positive square root of each factor to solve for $x$: $x = 3 \sqrt 7$