1. Stating the problem: Simplify the expression $$5\sqrt{50} + \sqrt{98}$$. 2. Recall the rule: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ and simplify square roots by factoring out perfect squares. 3. Simplify each term: - $$5\sqrt{50} = 5\sqrt{25 \times 2} = 5 \times 5 \sqrt{2} = 25\sqrt{2}$$ - $$\sqrt{98} = \sqrt{49 \times 2} = 7\sqrt{2}$$ 4. Combine like terms: $$25\sqrt{2} + 7\sqrt{2} = (25 + 7)\sqrt{2} = 32\sqrt{2}$$ 5. Final answer: $$32\sqrt{2}$$