Đáp án+Giải thích các bước giải:
`a)\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}`
`=\sqrt{5-2\sqrt{5.2}+2}+\sqrt{5+2\sqrt{5.2}+2}`
`=\sqrt{(sqrt5-sqrt2)^2}+sqrt{(sqrt5+sqrt2)^2}`
`=sqrt5-sqrt2+sqrt5+sqrt2`
`=2sqrt2`
`b)sqrt{11+2sqrt{18}}-sqrt{11-2sqrt{18}}`
`=\sqrt{9+2.sqrt{9.2}+2}-sqrt{9-2sqrt{9.2}+2}`
`=sqrt{(3+sqrt2)^2}-sqrt{(3-sqrt2)^2}`
`=3+sqrt2-3+sqrt2=2sqrt2`
`3a)sqrt{9+4sqrt2}-sqrt{9-4sqrt2}`
`=sqrt{8+2.2sqrt2+1}-sqrt{8-2.2.sqrt2+1}`
`=sqrt{(2sqrt2+1)^2}-sqrt{(2sqrt2-1)^2}`
`=2sqrt2+1-2sqrt2+1`
`=2`
`b)sqrt{14-6sqrt5}-sqrt{8-2sqrt{15}}`
`=sqrt{9-2.3.sqrt5+5}-sqrt{5-2sqrt{5.3}+3}`
`=sqrt{(3-sqrt5)^2}-sqrt{(sqrt5-sqrt3)^2}`
`=3-sqrt5-sqrt5+sqrt3`
`=3+sqrt3-2sqrt5`
`4a)c_1,A=sqrt{3+sqrt5}-sqrt{3-sqrt5}`
Vì `3+sqrt5>3-sqrt5`
`=>sqrt{3+sqrt5}-sqrt{3-sqrt5}>0`
`=>A>0`
`<=>A^2=3+sqrt5+3-sqrt5-2sqrt{(3+sqrt5)(3-sqrt5)}`
`<=>A^2=6-2sqrt{9-5}=6-2.2`
`<=>A^2=6-4=2`
`<=>A=sqrt2(do\ A>0)`
`c_2,sqrt2A=sqrt{6+2sqr5}-sqrt{6-2sqrt5}`
`<=>sqrt2A=sqrt{5+2sqrt5+1}-sqrt{5-2sqrt5+1}`
`<=>sqrt2A=sqrt{(sqrt5+1)^2}-sqrt{(sqrt5-1)^2}`
`<=>sqrt2A=sqrt5+1-sqrt5+1=2`
`<=>A=sqrt2`
`4b)c_1,B=sqrt{4-sqrt7}-sqrt{4+sqrt7}`
Vì `4+sqrt7>4-sqrt7`
`=>sqrt{4+sqrt7}-sqrt{4-sqrt7}>0`
`=>B<0``
`<=>B^2=4+sqrt7+4-sqrt7-2sqrt{(4+sqrt7)(4-sqrt7)}`
`<=>B^2=8-2sqrt{16-7}=8-2.3`
`<=>B^2=8-6=2`
`<=>B=-sqrt2(do\ A<0)`
`c_2,sqrt2B=sqrt{8+2sqrt7}-sqrt{8-2sqrt7}`
`<=>-sqrt2B=sqrt{7+2sqrt7+1}-sqrt{7-2sqrt7+1}`
`<=>-sqrt2B=sqrt{(sqrt7+1)^2}-sqrt{(sqrt7-1)^2}`
`<=>-sqrt2B=sqrt7+1-sqrt7+1=2`
`<=>A=-sqrt2`
