Answer
$-x^2\sqrt {2x}$
Work Step by Step
Before we can subtract these two numbers, we must transform them so that the radicands are the same. Only then can we perform the operation we are asked to do.
Let's expand the radicands in all of the radicals so that they are rewritten as the product of a perfect square and another number:
$\sqrt {8x^5} - \sqrt {18x^5}$ = $\sqrt {4 \cdot 2 \cdot x^4 \cdot x} - \sqrt {9 \cdot 2 \cdot x^4 \cdot x}$
We can now take the square roots of all the perfect squares:
$2x^2\sqrt {2x} - 3x^2\sqrt {2x}$
Subtract the coefficients, keeping the base as-is:
$-x^2\sqrt {2x}$
