[tex]5\sqrt{24}-3\sqrt{54}+\dfrac{2\sqrt{3}}{\sqrt2} = \\ \\ = 5\cdot\sqrt{2^2\cdot 6}-3\cdot\sqrt{3^2\cdot 6}+\dfrac{\sqrt2\cdot \sqrt2\cdot \sqrt3}{\sqrt2} = \\ \\ = 5\cdot \sqrt{2^2}\cdot \sqrt6-3\cdot \sqrt{3^2}\cdot \sqrt6+\sqrt2\cdot \sqrt3 = \\ \\= 5\cdot 2\sqrt6 - 3\cdot 3\sqrt6+\sqrt{2\cdot 3} = \\ \\ = 10\sqrt6-9\sqrt6+\sqrt6 = \\ \\ = \sqrt6+\sqrt6 = \\ \\ = 2\sqrt6[/tex]
