Answer
$(2x-15)\sqrt{2x}$.
Work Step by Step
Simplify each radical by factoring the radicand such that one of the factors is a perfect square:
$\sqrt{8x^3}-3\sqrt{50x}\\
=\sqrt{4x^2\cdot 2x}-3\sqrt{25\cdot 2x}\\
=\sqrt{(2x)^2\cdot 2x}-3\sqrt{5^2\cdot 2x}$
Use the rule $\sqrt{a\cdot b}=\sqrt{a} \cdot \sqrt{b}$ then simplify:
$=\sqrt{(2x)^2}\cdot \sqrt{2x}-3\cdot\sqrt{5^2}\cdot \sqrt{2x}$
$=2x\cdot \sqrt{2x}-3\cdot5\cdot \sqrt{2x}$
$=2x\sqrt{2x}-15\sqrt{2x}$
Factor out $\sqrt{2x}$.
$=\sqrt{2x}(2x-15)$
$=(2x-15)\sqrt{2x}$
Hence, the correct answer is $(2x-15)\sqrt{2x}$.
