Answer
$2x^5 \sqrt {6x}$
Work Step by Step
Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$
Here, $n$ refers as index.
$\sqrt {2x^7} \sqrt {12x^4}=\sqrt {(2x^7) (12x^4)}= \sqrt{24 x^{11}}$
The radical $\sqrt{24 x^{11}}$ can be further simplified by using product rule again.
Such as:
$\sqrt{24 x^{11}}=\sqrt {(4x^{10}) (6x)}=\sqrt {(2x^5)^2 (6x)}=2x^5 \sqrt {6x}$
