Answer
$25x\sqrt {2x}$.
Work Step by Step
The given expression is
$=5\sqrt {2x^3}+\frac{30x^3\sqrt {24x^2}}{3x^2\sqrt {3x}}$
Factor the radicands into square terms.
$=5\sqrt {2x^2\cdot x}+\frac{3\cdot 10x^2\cdot x\sqrt {2^2\cdot 3\cdot 2x^2}}{3x^2\sqrt {3x}}$
Simplify.
$=5\cdot x\sqrt {2x}+\frac{3x^2\cdot 10x\cdot 2x\sqrt { 3}\cdot \sqrt{2}}{3x^2\sqrt {3x}}$
Cancel out similar terms in the fraction.
$=5x\sqrt {2x}+20x\sqrt {2x}$
By using the distributive property:
$=(5+20)x\sqrt {2x}$
Simplify.
$=25x\sqrt {2x}$.
