1. The problem is to find the square root of 125. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. To simplify $\sqrt{125}$, factor 125 into its prime factors: $125 = 25 \times 5 = 5^2 \times 5$. 4. Using the property $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$, we get: $$\sqrt{125} = \sqrt{5^2 \times 5} = \sqrt{5^2} \times \sqrt{5} = 5\sqrt{5}$$ 5. Therefore, the simplified form of $\sqrt{125}$ is $5\sqrt{5}$. 6. This means the square root of 125 is $5$ times the square root of 5, which is an irrational number approximately equal to 11.1803.