1. The problem is to evaluate the expression $10|\sqrt{200}$, where $10$ is outside the square root and $\sqrt{200}$ is inside the root. 2. First, simplify the square root $\sqrt{200}$. We know that $200 = 100 \times 2$, so: $$\sqrt{200} = \sqrt{100 \times 2}$$ 3. Using the property of square roots $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we get: $$\sqrt{200} = \sqrt{100} \times \sqrt{2}$$ 4. Since $\sqrt{100} = 10$, substitute this back: $$\sqrt{200} = 10 \times \sqrt{2}$$ 5. Now multiply the $10$ outside the root by the simplified root expression: $$10 \times \sqrt{200} = 10 \times (10 \times \sqrt{2}) = 10 \times 10 \times \sqrt{2}$$ 6. Simplify the multiplication: $$10 \times 10 = 100$$ So the expression becomes: $$100 \times \sqrt{2}$$ 7. Therefore, the final simplified answer is: $$100\sqrt{2}$$