1. **State the problem:** Simplify the expression $$\sqrt{32} + \sqrt{50} - \sqrt{18}$$. 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 surd by factoring out perfect squares:** - $$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$$ - $$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$$ - $$\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2}$$ 4. **Substitute back into the expression:** $$4\sqrt{2} + 5\sqrt{2} - 3\sqrt{2}$$ 5. **Combine like terms:** $$ (4 + 5 - 3)\sqrt{2} = 6\sqrt{2}$$ **Final answer:** $$6\sqrt{2}$$