1. **State the problem:** Simplify the expression $3\sqrt{50} - \sqrt{8}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. **Simplify each square root:** - $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$ - $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$ 4. **Substitute back:** $$3\sqrt{50} - \sqrt{8} = 3 \times 5\sqrt{2} - 2\sqrt{2} = 15\sqrt{2} - 2\sqrt{2}$$ 5. **Combine like terms:** $$15\sqrt{2} - 2\sqrt{2} = (15 - 2)\sqrt{2} = 13\sqrt{2}$$ **Final answer:** $13\sqrt{2}$