3. The arithmetic mean of two positive numbers is $2 \sqrt{3}$, and the arithmetic square root of their product is $\sqrt{3}$. Then the larger number is greater than the smaller number by ( ).
(A) 4
(B) $2 \sqrt{3}$
(C) 6
(D) $3 \sqrt{3}$
3. C.

Let these two positive numbers be $x, y$. According to the conditions, we have
$$
\begin{array}{l}
\left\{\begin{array}{l}
x+y=4 \sqrt{3}, \\
x y=3
\end{array}\right. \\
\Rightarrow|x-y|=\sqrt{(x-y)^{2}}=6 .
\end{array}
$$