Answer
See explanations.
Work Step by Step
Step 1. The domain requirement for a square root function $f(x)=\sqrt x$ is that $x\geq0$ or $x$ be nonnegative.
Step 2. For $\sqrt a\sqrt b=\sqrt {ab}$ to be valid, each term needs to be defined, which requires values $a$ and $b$ to be nonnegative.
Step 3. In the case of $g(x)=\sqrt[3] x$, the domain contains all the real numbers, including negative numbers; thus the formula $\sqrt[3] a\sqrt[3] b=\sqrt[3] {ab}$ does not require nonnegative values of $a$ and $b$.
