1. **Problem statement:** Simplify the expression $$A = \sqrt{72} + \sqrt{50} - 2 \sqrt{18}$$. 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 term:** - $$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$$ - $$\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$$ - $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$ 4. **Substitute back:** $$A = 6\sqrt{2} + 5\sqrt{2} - 2 \times 3\sqrt{2}$$ 5. **Multiply and combine like terms:** $$A = 6\sqrt{2} + 5\sqrt{2} - 6\sqrt{2} = (6 + 5 - 6)\sqrt{2} = 5\sqrt{2}$$ 6. **Final answer:** $$A = 5\sqrt{2}$$