Multiply, and then simplify if possible. Assume that all variables represent positive real numbers. \( \sqrt{2 x}(\sqrt{2}-\sqrt{x}) \) \( \sqrt{2 x}(\sqrt{2}-\sqrt{x})=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)

To multiply the expression \( \sqrt{2x}(\sqrt{2} - \sqrt{x}) \), we can use the distributive property: \[ \sqrt{2x} \cdot \sqrt{2} - \sqrt{2x} \cdot \sqrt{x} \] Now, simplify each term: 1. The first term: \[ \sqrt{2x} \cdot \sqrt{2} = \sqrt{2 \cdot 2x} = \sqrt{4x} = 2\sqrt{x} \] 2. The second term: \[ \sqrt{2x} \cdot \sqrt{x} = \sqrt{2x^2} = \sqrt{2} \cdot x \] Putting it all together gives us: \[ \sqrt{2x}(\sqrt{2} - \sqrt{x}) = 2\sqrt{x} - \sqrt{2} \cdot x \] So the final simplified answer is: \[ 2\sqrt{x} - x\sqrt{2} \]