Please check my work here. I like my method, I don't want fractions instead of radicals.

The prob is: $\displaystyle 2\sqrt[3]{8x^2}\,+\,5\sqrt[3]{27x^2}\,-\,3\sqrt{x^3}$

That simplifies to $\displaystyle 4\sqrt[3]{x^2} + 15\sqrt[3]{x^2}\,-\,3x\sqrt{x}\;=\;\boxed{19\sqrt[3]{x^2}\,-\,3x\sqrt{x}}$

Lookin' good?