1. **State the problem:** Simplify the expression $$\sqrt{80} - \sqrt{45} + 10 \times \sqrt{5}$$. 2. **Recall the formula and rules:** The square root of a product can be written as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. Also, simplify square roots by factoring out perfect squares. 3. **Simplify each square root:** $$\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$ $$\sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5}$$ 4. **Rewrite the expression with simplified terms:** $$4\sqrt{5} - 3\sqrt{5} + 10\sqrt{5}$$ 5. **Combine like terms:** $$ (4 - 3 + 10) \sqrt{5} = 11 \sqrt{5}$$ **Final answer:** $$11 \sqrt{5}$$