1. **State the problem:** Simplify the expression $\sqrt{200} - \sqrt{32}$. 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:** $$\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2} = 10\sqrt{2}$$ $$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$$ 4. **Substitute back into the expression:** $$10\sqrt{2} - 4\sqrt{2}$$ 5. **Combine like terms:** $$\cancel{10}\sqrt{2} - \cancel{4}\sqrt{2} = (10 - 4)\sqrt{2} = 6\sqrt{2}$$ 6. **Final answer:** $$6\sqrt{2}$$