[tex]96|2\\48|2\\24|2\\12|2\\.\ 6|2\\.\ 3|3\\.\ 1|\\\\\sqrt{96}=\sqrt{2\cdot2\cdot2\cdot2\cdot2\cdot3}=\sqrt{2^2\cdot2^2\cdot2\cdot3}=\sqrt{2^2}\cdot\sqrt{2^2}\cdot\sqrt{2\cdot3}\\\\=2\cdot2\cdot\sqrt6=\boxed{4\sqrt6}\\\\used:\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\sqrt{a^2}=a\ for\ a\geq0[/tex]
