1. **State the problem:** Find the square root of 200. 2. **Formula and rules:** The square root of a number $x$ is a value $y$ such that $$y^2 = x.$$ We can simplify square roots by factoring out perfect squares. 3. **Factor 200:** $$200 = 100 \times 2$$ 4. **Use the property of square roots:** $$\sqrt{200} = \sqrt{100 \times 2} = \sqrt{100} \times \sqrt{2}$$ 5. **Evaluate the square root of 100:** $$\sqrt{100} = 10$$ 6. **Combine the results:** $$\sqrt{200} = 10 \times \sqrt{2} = 10\sqrt{2}$$ 7. **Final answer:** $$\boxed{10\sqrt{2}}$$