## Intermediate Algebra (12th Edition)

(a) We know that $-\sqrt{-x}$ is not a real number because $-x$ is negative (since $x$ is positive) and we can't take the square root of a negative number ($\sqrt{x}$ is undefined for $x\lt0$). (b) We know that $-\sqrt{x}$ is negative because $\sqrt{x}$ is always positive, by definition.