Answer
$26x \sqrt {2}$
Work Step by Step
The radicals have the same index but different radicands (expression inside the radical sign) so they not similar. Simplify both radicals by factoring each radicand so that at least one of the factors is a square.
For the first radical, $32=16(2)=4^2(2)$ so:
$2\sqrt{32x^2}=2 \sqrt {(4^2)(2)(x^2)}$
Take out the square root of $4^2$ and $x^2$ to obtain:
$=(2)(4)(x)\sqrt {2}\\
=8\sqrt{2}$
For the second radical, $72=36(2)=6^2(2)$ so
$3\sqrt{72x^2}=3 \sqrt {(6^2)(2)(x^2)}$
Take out the square root of $6^2$ and $x^2$ to obtain:
$=(3)(6)(x)\sqrt {2}$
$=18x \sqrt {2}$
Thus, the given expression is equivalent to:
$$8x\sqrt2+18x\sqrt2$$
This time, the radicals have the same index and the same radicand so they are now similar.
Perform the operation by adding the coefficients and retaining the radical to obtain:
$=(8x+18x)\sqrt {2}\\
=26x\sqrt2$