#### Answer

$4 \sqrt 3$

#### 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:
$\frac{3}{x} = \frac{x}{16}$
Use the cross products property to get rid of the fractions:
$x^2 = 48$
Rewrite $48$ as the product of a perfect square and another factor:
$x^2 = 16 • 3$
Take the positive square root of each factor to solve for $x$:
$x = 4 \sqrt 3$