Multiply, and then simplify if possible. Assume that all variables represent positive real numbers. \( \sqrt{3 x}(\sqrt{3}-\sqrt{x}) \) \( \sqrt{3 x}(\sqrt{3}-\sqrt{x})=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)

To multiply the expression, we can apply the distributive property: \[ \sqrt{3x}(\sqrt{3} - \sqrt{x}) = \sqrt{3x} \cdot \sqrt{3} - \sqrt{3x} \cdot \sqrt{x} \] Next, we simplify each term separately: 1. \( \sqrt{3x} \cdot \sqrt{3} = \sqrt{3 \cdot 3x} = \sqrt{9x} = 3\sqrt{x} \) 2. \( \sqrt{3x} \cdot \sqrt{x} = \sqrt{3 \cdot x \cdot x} = \sqrt{3x^2} = \sqrt{3} \cdot x \) Putting these together, we have: \[ \sqrt{3 x}(\sqrt{3}-\sqrt{x}) = 3\sqrt{x} - \sqrt{3} \cdot x \] Thus, the simplified answer is: \[ 3\sqrt{x} - \sqrt{3}x \]