1. The problem is to simplify the expression $\sqrt{-x^2}$.\n\n2. Recall that $x^2$ is always non-negative for any real number $x$, so $-x^2$ is non-positive (less than or equal to zero).\n\n3. The square root of a negative number is not a real number; it is an imaginary number. We use the imaginary unit $i$ where $i^2 = -1$.\n\n4. Rewrite the expression inside the square root as $-1 \cdot x^2$. So, $\sqrt{-x^2} = \sqrt{-1 \cdot x^2}$.\n\n5. Using the property of square roots, $\sqrt{ab} = \sqrt{a} \cdot \sqrt{b}$, we get $\sqrt{-1} \cdot \sqrt{x^2}$.\n\n6. We know $\sqrt{-1} = i$ and $\sqrt{x^2} = |x|$ (the absolute value of $x$).\n\n7. Therefore, $\sqrt{-x^2} = i |x|$.\n\nFinal answer: $$\sqrt{-x^2} = i |x|$$