The problem asks us to combine the expression $3\sqrt{3x} + 4\sqrt{75x} + 3\sqrt{48x}$, assuming that $x$ represents a nonnegative real number. We need to simplify the expression and type an exact answer using radicals as needed.

1. Problem Description

The problem asks us to combine the expression $3\sqrt{3x} + 4\sqrt{75x} + 3\sqrt{48x}$, assuming that $x$ represents a nonnegative real number. We need to simplify the expression and type an exact answer using radicals as needed.

2. Solution Steps

We first simplify the radicals $\sqrt{75x}$ and $\sqrt{48x}$.

$\sqrt{75x} = \sqrt{25 \cdot 3x} = \sqrt{25} \cdot \sqrt{3x} = 5\sqrt{3x}$

$\sqrt{48x} = \sqrt{16 \cdot 3x} = \sqrt{16} \cdot \sqrt{3x} = 4\sqrt{3x}$

Substituting these simplified expressions back into the original expression, we have:

$3\sqrt{3x} + 4\sqrt{75x} + 3\sqrt{48x} = 3\sqrt{3x} + 4(5\sqrt{3x}) + 3(4\sqrt{3x})$

$= 3\sqrt{3x} + 20\sqrt{3x} + 12\sqrt{3x}$

$= (3 + 20 + 12)\sqrt{3x}$

$= 35\sqrt{3x}$

3. Final Answer

$35\sqrt{3x}$