Question

Căn (8-4căn3) - căn (14+8căn3) Rút gọn và tính

Answer 1

`sqrt{8-4sqrt3}-sqrt{14+8sqrt3}`

`=sqrt{2(4-2sqrt3)}-sqrt{2(7+4sqrt3)}`

`=sqrt{2(3-2sqrt3+1)}-sqrt{2(4+2.2.sqrt3+3)}`

`=sqrt{2(sqrt3-1)^2}-sqrt{2(2+sqrt3)^2}`

`=sqrt2(sqrt3-1)-sqrt2(2+sqrt3)`

`=sqrt6-sqrt2-2sqrt2-sqrt6`

`=-3sqrt2`

Answer 2

Answer 3

\(\sqrt{8-4\sqrt{3}}-\sqrt{14+8\sqrt{3}}\)

\(=\sqrt{\left(\sqrt{6}\right)^2-2.\sqrt{6}.\sqrt{2}+\left(\sqrt{2}\right)^2}-\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2}.\sqrt{6}+\left(\sqrt{6}\right)^2}\)

\(=\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}-\sqrt{\left(2\sqrt{2}+\sqrt{6}\right)^2}=\sqrt{6}-\sqrt{2}-2\sqrt{2}-\sqrt{6}=-3\sqrt{2}\)