Answer
$9\sqrt{2}$.
Work Step by Step
Factor the radicands using the greatest perfect square factors.
$\Rightarrow 4\sqrt{72}-3\sqrt{50}=4\sqrt{2^2\cdot 3^2\cdot 2}-3\sqrt{5^2\cdot 2}$
Take the square root of each factor.
$\Rightarrow 4\sqrt{2^2}\cdot \sqrt{3^2}\cdot \sqrt{2}-3\sqrt{5^2}\cdot \sqrt{2}$
$\Rightarrow 4\cdot 2\cdot 3\cdot \sqrt{2}-3\cdot 5\cdot \sqrt{2}$
Multiply.
$\Rightarrow 24\sqrt{2}-15\sqrt{2}$
Apply the distributive property.
$\Rightarrow (24-15)\sqrt{2}$
Simplify.
$\Rightarrow 9\sqrt{2}$.
