Đáp án:
`(2sqrt6-4sqrt3+5sqrt2-1/4sqrt3)*3sqrt6`
`=2sqrt6*3sqrt6-4sqrt3*3sqrt6+5sqrt2*3sqrt6-1/4sqrt3*3sqrt6`
`=36-36sqrt2+30sqrt3-(3sqrt2)/4`
`=(144-147sqrt2+120sqrt3)/4`
`sqrt{18}/sqrt2-sqrt{12}/sqrt3`
`=sqrt9-sqrt4`
`=3-2=1`
`1/2(sqrt6+sqrt5)^2-1/4*sqrt{120}-sqrt{15}/2`
`=1/2(11+2sqrt{30})-1/4*2sqrt{30}-sqrt{15}/2`
`=11/2+sqrt{30}-sqrt{30}/2-sqrt{15}/2`
`=(11+sqrt{30}-sqrt{15})/2`.