Câu b và d rút gọn ạ

Đáp án + Giải thích các bước giải:

 `b)`

`(9-2\sqrt{3})/(3\sqrt{6}-2\sqrt{2})+3/(3+\sqrt{6})`

`=((9-2\sqrt{3})(3\sqrt{6}+2\sqrt{2}))/((3\sqrt{6}+2\sqrt{2})(3\sqrt{6}-2\sqrt{2})) +(3(3-\sqrt{6}))/((3+\sqrt{6})(3-\sqrt{6}))`

`= (27\sqrt{6} +18\sqrt{2}-18\sqrt{2}-4\sqrt{6})/(54-8) +(3(3-\sqrt{6}))/(9-6)`

`= (23\sqrt{6})/46 +(3-\sqrt{6})`

`= (\sqrt{6})/2 +3-\sqrt{6}`

`= (\sqrt{6})/2 +(2(3-\sqrt{6}))/2`

`= (\sqrt{6}+6-2\sqrt{6})/2`

`= (6-\sqrt{6})/2`

`d)`

`\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}`

`= \sqrt{9-6\sqrt{6}+6}+\sqrt{24-12\sqrt{6}+9}`

`= \sqrt{3^2-2.3.\sqrt{6}+(\sqrt{6})^2}+\sqrt{(2\sqrt{6})^2-2.2\sqrt{6}.3+3^2}`

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

`= |3-\sqrt{6}|+|2\sqrt{6}-3|`

`= 3-\sqrt{6}+2\sqrt{6}-3`

`= \sqrt{6}`