1. **State the problem:** Simplify the expression $5\sqrt{8} + \sqrt{18}$. 2. **Recall the rule:** To simplify expressions with square roots, factor the radicand (the number inside the root) into perfect squares and simplify. 3. **Simplify each term:** - $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$ - $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$ 4. **Substitute back:** $$5\sqrt{8} + \sqrt{18} = 5 \times 2\sqrt{2} + 3\sqrt{2} = 10\sqrt{2} + 3\sqrt{2}$$ 5. **Combine like terms:** $$10\sqrt{2} + 3\sqrt{2} = (10 + 3)\sqrt{2} = 13\sqrt{2}$$ **Final answer:** $13\sqrt{2}$