`sqrt((6-2sqrt3)/(sqrt8-sqrt4))`
`=sqrt((2sqrt3(sqrt3-1))/(sqrt4(sqrt2-1))`
`=sqrt((2sqrt3(sqrt3-1))/(2(sqrt2-1))`
`=sqrt((sqrt3(sqrt3-1))/(sqrt2-1))=sqrt((3-sqrt3)/(sqrt2-1))`
`=sqrt(((3-sqrt3)(sqrt2+1))/((sqrt2-1)(sqrt2+1))`
`=sqrt((3sqrt2+3-sqrt6-sqrt3)/1)`
`=sqrt(3sqrt2+3-sqrt6-sqrt3)`
$$$$
`1/(sqrt5+sqrt3)-1/(sqrt5-sqrt3)`
`=(sqrt5-sqrt3-(sqrt5+sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))`
`=(sqrt5-sqrt3-sqrt5-sqrt3)/(5-3)`
`=(-2sqrt3)/2=-sqrt3`