`a)sqrt{12}-3sqrt3+sqrt{48}`
`=2sqrt3-3sqrt3+4sqrt3`
`=3sqrt3`
`b)4sqrt{(2-sqrt3)^2}+2sqrt{(2+sqrt3)^2}+2sqrt3`
`=4(2-sqrt3)+2(2+sqrt3)+2sqrt3`
`=8-4sqrt3+4+2sqrt3+2sqrt3`
`=12`
`c)1/(2-sqrt3)+1/(2+sqrt3)`
`=(2+sqrt3)/((2-sqrt3)(2+sqrt3))+(2-sqrt3)/((2+sqrt3)(2-sqrt3))`
`=(2+sqrt3)/(4-3)+(2-sqrt3)/(4-3)`
`=2+sqrt3+2-sqrt3`
`=4`
`d)sqrt{5-2sqrt6}+sqrt{7-2sqrt6}+sqrt2-sqrt6+1`
`=sqrt{3-2sqrt{3.2}+2}+sqrt{6-2sqrt6+1}+sqrt2-sqrt6+1`
`=sqrt{(sqrt3-sqrt2)^2}+sqrt{(sqrt6-1)^2}+sqrt2-sqrt6+1`
`=sqrt3-sqrt2+sqrt6-1+sqrt2-sqrt6+1`
`=sqrt3`
