Answer
$6x\sqrt{x}$
Work Step by Step
Use the rule $\sqrt[n]{a} \cdot \sqrt[n]{b}=\sqrt[n]{a\cdot b},\quad a,b>0$ to obtain:.
$\sqrt{3x^2}\sqrt{12x}=\sqrt{3x^2\cdot 12x}$
Simplify.
$=\sqrt{36x^2x}$
Use $36=6^2$.
$=\sqrt{6^2x^2x}$
Separate using the rule $\sqrt[n]{a\cdot b}=\sqrt[n]{a} \cdot \sqrt[n]{b}, a,b>0$ to obtain:.
$=\sqrt{6^2x^2}\sqrt{x}$
Simplify.
$=6x\sqrt{x}$
Hence, the correct answer is $6x\sqrt{x}$.
