1. **State the problem:** Find the square root of 1000. 2. **Formula and rules:** The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. **Calculate the square root:** $$\sqrt{1000} = \sqrt{10^3} = \sqrt{10^2 \times 10} = 10 \sqrt{10}$$ 4. **Simplify the expression:** The square root of 1000 simplifies to $10 \sqrt{10}$. 5. **Approximate the value:** Since $\sqrt{10} \approx 3.162$, then $$10 \times 3.162 = 31.62$$ **Final answer:** $$\sqrt{1000} = 10 \sqrt{10} \approx 31.62$$