[latex]2 sqrt{48}-3 sqrt{108}= \ 48|2............108|2 \ 24|2..............54|2 \ 12|2..............27|3 \ ..6|2................9|3 \ ..3|3................3|3 \ sqrt{48}= sqrt{2^4*3}=2^2*sqrt{3}=4 sqrt{3} \ sqrt{108}= sqrt{2^2*3^3}=2*3*sqrt{3} =6 sqrt{3} \ 2*4 sqrt{3}-3*6 sqrt{3}= \ 8 sqrt{3}-18 sqrt{3}=oxed{-10 sqrt{3} } [/latex]