#### Answer

$x = 2$

#### Work Step by Step

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:
$\frac{\sqrt 8}{x} = \frac{x}{\sqrt 2}$
Use the cross products property to get rid of the fractions:
$x^2 = \sqrt 16$
Take the square root of $16$ to simplify:
$x^2 = 4$
Take the positive square root to solve for $x$:
$x = 2$