1. The problem is to find the square root of 1000. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. We use the formula $\sqrt{1000}$. 4. Simplify $\sqrt{1000}$ by factoring 1000 into prime factors: $1000 = 10^3 = (2 \times 5)^3 = 2^3 \times 5^3$. 5. Using the property $\sqrt{a^2 \times b} = a \sqrt{b}$, we take out pairs of factors: $$\sqrt{1000} = \sqrt{2^3 \times 5^3} = \sqrt{(2^2 \times 5^2) \times (2 \times 5)} = \sqrt{(10^2) \times 10} = 10 \sqrt{10}$$ 6. Therefore, the square root of 1000 is $10 \sqrt{10}$, which is approximately 31.622.