The property $\sqrt[\phantom{2}]{a}*\sqrt[\phantom{2}]{b}=\sqrt[\phantom{2}]{ab}$ is true under which of the following conditions?

Choose the correct statement below.

A$.$ The product ab must be greater than or equal to zero.

B$.$ Either $a0$ or $b0.$

C$.$ Both a and $b$ must be greater than or equal to zero.

D$.$ Both a and $b$ must be nonzero.