1. **State the problem:** Simplify the expression $2x\sqrt{2}$. 2. **Recall the rules:** The square root of 2, $\sqrt{2}$, is an irrational number approximately equal to 1.414. When multiplying, constants and variables can be combined by multiplication. 3. **Multiply the constants:** $2 \times \sqrt{2} = 2\sqrt{2}$. 4. **Include the variable:** The expression remains $2x\sqrt{2}$ since $x$ is a variable and cannot be simplified further without its value. **Final answer:** $2x\sqrt{2}$