#### Answer

$$4x\sqrt 3x$$

#### Work Step by Step

We can use the product rule for square roots to rewrite the radicand as a product of the greatest perfect square factor and another factor. We can see that the radicand $48x^3$ can be broken down into two factors: the perfect square $16x^2$ and $3x$:
$$(\sqrt 16x^2)(\sqrt 3x)$$
Because $16x^2$ is a perfect square, we go ahead and simplify the expression by taking the square root of $16x^2$, which is $4x$:
$$4x\sqrt 3x$$