Đáp án+Giải thích các bước giải:
`sqrt{11+2sqrt{18}}`
`=sqrt{9+2sqrt(9.2)+2}`
`=sqrt{(3+sqrt2)^2}`
`=3+sqrt2`
`sqrt{14-6sqrt5}`
`=sqrt{9-2.3.sqrt5+5}`
`=sqrt{(3-sqrt5)^2}`
`=3-sqrt5`
`sqrt{17-12sqrt2}`
`=sqrt{9-2.3.2sqrt+8}`
`=sqrt{(3-2sqrt2)^2}`
`=3-2sqrt2`
`sqrt{27-12sqrt5}`
`=sqrt{3(9-4sqrt5)}`
`=sqrt{3(5-2.2.sqrt5+4)}`
`=sqrt{3(sqrt5-2)^2}`
`=sqrt3(sqrt5-2)`
`=sqrt{15}-2sqrt3`
`sqrt{28-12sqrt5}`
`=sqrt{2(14-6sqrt5)}`
`=sqrt{2(9-2.3.sqrt5+5)}`
`=sqrt{2(3-sqrt5)^2}`
`=sqrt2(3-sqrt5)`
`=3sqrt2-sqrt(10)`
`sqrt{7-3sqrt5}`
`=sqrt{(14-6sqrt5).2}`
`=sqrt{1/22(9-2.3.sqrt5+5)}`
`=sqrt{1/2(3-sqrt5)^2}`
`=(3-sqrt5)/sqrt2`
`=(3sqrt2-sqrt(10))/2`
`sqrt{4+sqrt{15}}`
`=sqrt{(8+2sqrt(15))/2}`
`=sqrt{(5+2sqrt{5.3}+3)/2}`
`=sqrt{(sqrt5+sqrt3)^2/2}`
`=(sqrt5+sqrt3)/sqrt2`
`=sqrt{10}+sqrt6`