Căn(32+ 12 căn7) Căn(18-6 căn5)

1 câu trả lời

a) `\sqrt{32+12\sqrt{7}}`

`=\sqrt{2}.\sqrt{16+6\sqrt{7}}`

`=\sqrt{2}.\sqrt{9+2.3.\sqrt{7}+7}`

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

`=\sqrt{2}.|3+\sqrt{7}|`

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

`=3\sqrt{2}+\sqrt{14}`

b) `\sqrt{18-6\sqrt{5})`

`=\sqrt{3}.\sqrt{6-2\sqrt{5}}`

`=\sqrt{3}.\sqrt{5-2\sqrt{5}+1}`

`=\sqrt{3}.\sqrt{(\sqrt{5}-1)^2}`

`=\sqrt{3}.|\sqrt{5}-1|`

`=\sqrt{3}.(\sqrt{5}-1)`

`=\sqrt{15}-\sqrt{3}`