1. **State the problem:** Simplify the expression $8x^{1/2}$. 2. **Recall the rule:** The expression $x^{1/2}$ means the square root of $x$, so $x^{1/2} = \sqrt{x}$. 3. **Rewrite the expression:** Replace $x^{1/2}$ with $\sqrt{x}$ to get $8\sqrt{x}$. 4. **Final answer:** The simplified form of $8x^{1/2}$ is $$8\sqrt{x}$$.