Question

Rút gọn

a, √21+3√48 - √21-3√48

b, √-2√10 - √7 + 2√10

c.ơn các bạn trước :3

Answer 1

`a)Đặt \, A=sqrt{21+3sqrt{48}}-sqrt{21-3sqrt{48}}`

Vì `21+3sqrt{48}>21-3sqrt{48}`

`=>sqrt{21+3sqrt{48}}-sqrt{21-3sqrt{48}}>0`

Hay `A>0`

`<=>A^2=21+3sqrt{48}+21-3sqrt{48}-2sqrt{21^2-9.48}`

`<=>A^2=42-2sqrt{9}=32-2.3=26`

`<=>A=sqrt{26}(do \ A>0)`

Answer 2

b)Chắc đề là như này:

`sqrt{7-2sqrt{10}}-sqrt{7+2sqrt{10}}`

`=sqrt{5-2sqrt{5}.sqrt2+2}-sqrt{5+2sqrt{5}.sqrt2+2}`

`=sqrt{(sqrt5-sqrt2)^2}-sqrt{(sqrt5+sqrt2)^2}`

`=sqrt5-sqrt2-sqrt5-sqrt2=-2sqrt2`

Answer 3

a) Ta có: \(\sqrt{21+3\sqrt{48}}-\sqrt{21-3\sqrt{48}}\)

\(=\sqrt{12+2\cdot2\sqrt{3}\cdot3+9}-\sqrt{12-2\cdot2\sqrt{3}\cdot3+9}\)

\(=2\sqrt{3}+3-2\sqrt{3}+3\)

=6

b) Ta có: \(\sqrt{7-2\sqrt{10}}-\sqrt{7+2\sqrt{10}}\)

\(=\sqrt{5}-\sqrt{2}-\sqrt{5}-\sqrt{2}\)

\(=2\sqrt{2}\)