Answer: [tex]\bold{-19\sqrt{6}+8\sqrt{5}}[/tex]
Step-by-step explanation:
[tex].\quad 3\sqrt{24}-7\sqrt{54}-\sqrt{96}+4\sqrt{20}\\\\=3\sqrt{\underline{2\cdot 2}\cdot2 \cdot3}-7\sqrt{2\cdot 3\cdot\underline{3\cdot 3}}-\sqrt{\underline{2\cdot 2}\cdot \underline{2\cdot 2}\cdot 2\cdot 3}+4\sqrt{\underline{2\cdot 2}\cdot 5}\\\\=2\cdot 3\sqrt{2 \cdot3}-3\cdot 7\sqrt{2\cdot 3}-2\cdot 2\sqrt{2\cdot 3}+2\cdot 4\sqrt{5}\\\\=6\sqrt{6}-21\sqrt{6}-4\sqrt{6}+8\sqrt{5}\\\\=-19\sqrt{6}+8\sqrt{5}[/tex]
