Answer
$F$
Work Step by Step
Rewrite the radicands so that they are products of a perfect square and another factor:
$4\sqrt {9 \cdot 2 \cdot x^2 \cdot x^2} - 3\sqrt {36 \cdot 2 \cdot x^2 \cdot x^2}$
Take the square roots of the perfect squares in the radicands:
$4 \cdot 3 \cdot x \cdot x \sqrt {2} - 3 \cdot 6 \cdot x \cdot x \sqrt {2}$
Simplify:
$12x^2 \sqrt {2} - 18x^2 \sqrt {2}$
The radicands and indices are the same; therefore, we can subtract the two expressions together:
$\begin{align*}
12x^2\sqrt2-18x^2\sqrt2&=(12x^2-18x^2)\sqrt2\\
&=-6x^2 \sqrt {2}
\end{align*}$
The answer corresponds to option $F$.
