Answer
$$(\sqrt3)^{1/2}\times(\sqrt{12})^{1/2}=\sqrt6$$
Work Step by Step
$$(\sqrt3)^{1/2}\times(\sqrt{12})^{1/2}$$
As $\sqrt3\gt0$ and $\sqrt{12}\gt0$, we can apply the law of exponents here.
Applying this law: $$a^x\times b^x=(ab)^x$$ we have
$$(\sqrt3)^{1/2}\times(\sqrt{12})^{1/2}=(\sqrt3\times\sqrt{12})^{1/2}=(\sqrt{36})^{1/2}=6^{1/2}=\sqrt6$$
