Đáp án+Giải thích các bước giải:
`sqrt{5+sqrt{21}}+sqrt{5-sqrt{21}}-2sqrt{4-sqrt7}`
`=sqrt{(10+2sqrt{21})/2}+sqrt{(10-2sqrt{21})/2}-2sqrt{(8-2sqrt7)/2}`
`=sqrt{(7+2sqrt7 sqrt3+3)/2}+sqrt{(7-2sqrt7 sqrt3+3)/2}-2sqrt{(7-2sqrt7+1)/2}`
`=sqrt{(sqrt7+sqrt3)^2/2}+sqrt{(sqrt7-sqrt3)^2/2}-2sqrt{(sqrt7-1)^2/2}`
`=(sqrt7+sqrt3)/sqrt2+(sqrt7-sqrt3)/sqrt2-2((sqrt7-1)/sqrt2)`
`=(sqrt7+sqrt3+sqrt7-sqrt3)/sqrt2-sqrt2(sqrt7-1)`
`=(2sqrt7)/sqrt2-sqrt{14}+sqrt2`
`=sqrt{14}-sqrt{14}+sqrt2`
`=sqrt2.`