1. The problem is to simplify the expression $\sqrt{25x^2}$.\n\n2. Recall the property of square roots: $\sqrt{a^2} = |a|$, which means the square root of a square is the absolute value of the base.\n\n3. Apply this property to the expression: $\sqrt{25x^2} = \sqrt{25} \cdot \sqrt{x^2}$.\n\n4. Simplify each square root: $\sqrt{25} = 5$ and $\sqrt{x^2} = |x|$.\n\n5. Therefore, $\sqrt{25x^2} = 5|x|$.\n\nFinal answer: $5|x|$