Answer
$2x^2 \sqrt {10x}$
Work Step by Step
Apply product rule: $\sqrt[n] p \sqrt[n] q=\sqrt[n]{pq}$
Here, $n$ refers as index.
$\sqrt {5x^3} \sqrt[n] {8x^2}=\sqrt {(5x^3) (8x^2)}= \sqrt{40 x^5}$
The radical $\sqrt{40 x^5}$ can be further simplified by using product rule again.
Such as:
$\sqrt{40 x^5}=\sqrt {(4x^4) (10x)}=\sqrt {(2x^2)^2 (10x)}=2x^2 \sqrt {10x}$
