Đáp án + Giải thích các bước giải:
Bài `4` :
`a)` `sqrt75-sqrt(5 1/3)+9/2sqrt(2 2/3)+2sqrt27`
`=5sqrt3-sqrt(16/3)+9/2sqrt(8/3)+2*3sqrt3`
`=5sqrt3-(sqrt16)/(sqrt3)+9/2*(sqrt8)/sqrt3+6sqrt3`
`=5sqrt3-4/sqrt3+9/2*(sqrt8*sqrt3)/3+6sqrt3`
`=5sqrt3-(4sqrt3)/3+9/2*(sqrt24)/3+6sqrt3`
`=5sqrt3-4/3sqrt3+3sqrt6+6sqrt3`
`=5sqrt3-4/3sqrt3+3sqrt2*sqrt3+6sqrt3`
`=sqrt3(5-4/3+3sqrt2+6)=sqrt3(29/3+3sqrt2)=(29sqrt3)/3+3sqrt6`
`=(29sqrt3)/3+(9sqrt6)/3=(29sqrt3+9sqrt6)/3`
`b)` `sqrt48+sqrt(5 1/3)+2sqrt75-5sqrt(1 1/3)`
`=4sqrt3+sqrt(16/3)+2*5sqrt3-5sqrt(4/3)`
`=4sqrt3+4/sqrt3+10sqrt3-5*2/sqrt3`
`=4sqrt3+(4sqrt3)/3+10sqrt3-10/sqrt3`
`=4sqrt3+4/3sqrt3+10sqrt3-10/3sqrt3=sqrt3(4+4/3+10-10/3)=12sqrt3`.
