Answer
$-8\sqrt {3}$
Work Step by Step
Before we can subtract these two numbers, we must transform them so that the radicals are the same. Only then can we perform the operation we are asked to do.
Expand the radicands into their constituent factors in both radicals. We want one of the factors to be a perfect square so that we can take it out from under the radical sign.
$2\sqrt {4 \cdot 3} - 4\sqrt {9 \cdot 3}$
Take the square roots to take terms out from under the radical sign:
$2 \cdot 2\sqrt {3} - 4 \cdot 3\sqrt {3}$
Simplify by multiplying:
$4\sqrt {3} - 12\sqrt {3}$
Finally, we can perform the operation in the original problem because we now have the same radical in the two terms. We just add the coefficients and keep the radical as-is:
$-8\sqrt {3}$
