[tex]54=9\cdot6\\24=4\cdot6\\\\3\sqrt{54}-4\sqrt{24}=3\sqrt{9\cdot6}-4\sqrt{4\cdot6}=3\cdot\sqrt9\cdot\sqrt6-4\cdot\sqrt4\cdot\sqrt6\\\\=3\cdot3\cdot\sqrt6-4\cdot2\cdot\sqrt6=9\sqrt6-8\sqrt6=1\sqrt6=\sqrt6\\\\\text{Answer:}\ \sqrt6\\\\\text{Used:}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b} [/tex]
