Answer
$47x\sqrt {2x}$.
Work Step by Step
The given expression is
$=7\sqrt {2x^3}+\frac{40x^3\sqrt {150x^2}}{5x^2\sqrt {3x}}$
Divide the radicands and retain the common index.
$=7\sqrt {2x^3}+\frac{40x^3}{5x^2}\cdot \sqrt {\frac{150x^2}{3x}}$
Factor the radicands into square terms.
$=7\sqrt {2x^2\cdot x}+\frac{40x^3}{5x^2}\cdot \sqrt {\frac{5^2\cdot 2\cdot 3\cdot x^2}{3x}}$
Cancel out similar terms.
$=7\sqrt {2x^2\cdot x}+8x\cdot \sqrt {5^2\cdot 2\cdot x}$
Simplify.
$=7x\sqrt {2x}+8x\cdot 5\cdot \sqrt { 2 x}$
$=7x\sqrt {2x}+40x\sqrt { 2x}$
Apply the distributive property.
$=(7+40)x\sqrt {2x}$
Simplify.
$=47x\sqrt {2x}$.
