√((√3-√7 )^2 ).√(2/(5-√21)) Nhờ mọi người giải giúp ạ

Đáp án:

`sqrt{(sqrt{3}-sqrt{7})^2}.sqrt{2/(5-sqrt{21})}=2`

Giải thích các bước giải:

`sqrt{(sqrt{3}-sqrt{7})^2}.sqrt{2/(5-sqrt{21})}`
`=|sqrt{3}-sqrt{7}|.sqrt{(2.(5+sqrt{21}))/((5-sqrt{21})(5+sqrt{21}))}`
`=(sqrt{7}-sqrt{3}).sqrt{(2.(5+sqrt{21}))/(25-21)}` ( `|sqrt{3}-sqrt{7}|=sqrt{7}-sqrt{3}` vì `sqrt{3}<sqrt{7}`)
`=(sqrt{7}-sqrt{3}).sqrt{(2.(5+sqrt{21}))/(4)}`
`=(sqrt{7}-sqrt{3}).sqrt{(10+2sqrt{21})/4}`
`=(sqrt{7}-sqrt{3}).sqrt{((sqrt{7})^2+2.sqrt{7}.sqrt{3}+(sqrt{3})^2)/4}`
`=(sqrt{7}-sqrt{3}).sqrt{((sqrt{7}+sqrt{3})^2)/4}`
`=(sqrt{7}-sqrt{3}) . sqrt{(sqrt{7}+sqrt{3})^2}/sqrt{4}`
`=(sqrt{7}-sqrt{3}) . |sqrt{7}+sqrt{3}|/2`
`=(sqrt{7}-sqrt{3}) . (sqrt{7}+sqrt{3})/2`
`=((sqrt{7}-sqrt{3})(sqrt{7}+sqrt{3}))/2`
`=(7-3)/2`
`=4/2`
`=2`

Đáp án:

`2` 

Giải thích các bước giải:

`\qquad \sqrt{(\sqrt{3}-\sqrt{7})^2}.\sqrt{2/{(5-\sqrt{21})}`

`=|\sqrt{3}-\sqrt{7}|.\sqrt{{2.(5+\sqrt{21})}/{(5-\sqrt{21}).(5+\sqrt{21})}}`

`=(\sqrt{7}-\sqrt{3}). \sqrt{{10+2\sqrt{21}}/{5^2-21}}` (vì `\sqrt{7}>\sqrt{3}`)

`=(\sqrt{7}-\sqrt{3}).\sqrt{{7+2.\sqrt{7}.\sqrt{3}+3}/{4}}`

`=(\sqrt{7}-\sqrt{3}).\sqrt{{(\sqrt{7}+\sqrt{3})^2}/{2^2}}`

`=(\sqrt{7}-\sqrt{3}).{\sqrt{7}+\sqrt{3}}/2`

`={(\sqrt{7}-\sqrt{3}).(\sqrt{7}+\sqrt{3})}/2`

`={7-3}/2=2`