Hướng dẫn trả lời:

5) `{1}/{sqrt{8} + sqrt{7}} + sqrt{175} - 2sqrt{2}`

`= {1}/{sqrt{2^3} + sqrt{7}} + sqrt{5^2cdot7} - 2sqrt{2}`

`= {1}/{2sqrt{2} + sqrt{7}} + 5sqrt{7} - 2sqrt{2}`

`= {1cdot(2sqrt{2} - sqrt{7})}/{(2sqrt{2} + sqrt{7})cdot(2sqrt{2} - sqrt{7})} + 5sqrt{7} - 2sqrt{2}`

`= {2sqrt{2} - sqrt{7}}/{(2sqrt{2})^2 - (sqrt{7})^2} + 5sqrt{7} - 2sqrt{2}`

`= {2sqrt{2} - sqrt{7}}/{8 - 7} + 5sqrt{7} - 2sqrt{2}`

`= {2sqrt{2} - sqrt{7}}/{1} + 5sqrt{7} - 2sqrt{2}`

`= (2sqrt{2} - sqrt{7}) + 5sqrt{7} - 2sqrt{2}`

`= 2sqrt{2} - sqrt{7} + 5sqrt{7} - 2sqrt{2}`

`= (2sqrt{2} - 2sqrt{2}) + (- sqrt{7} + 5sqrt{7})`

`= 4sqrt{7}`

6) `{2}/{sqrt{7} - sqrt{6}} - sqrt{28} + sqrt{54}`

`= {2cdot(sqrt{7}+ sqrt{6})}/{(sqrt{7} - sqrt{6})cdot(sqrt{7}+ sqrt{6})} - sqrt{2^2cdot7} + sqrt{3^2cdot6}`

`= {2sqrt{7} + 2sqrt{6}}/{(sqrt{7})^2 - (sqrt{6})^2} - 2sqrt{7} + 3sqrt{6}`

`= {2sqrt{7} + 2sqrt{6}}/{7 - 6} - 2sqrt{7} + 3sqrt{6}`

`= {2sqrt{7} + 2sqrt{6}}/{1} - 2sqrt{7} + 3sqrt{6}`

`= (2sqrt{7} + 2sqrt{6}) - 2sqrt{7} + 3sqrt{6}`

`= 2sqrt{7} + 2sqrt{6} - 2sqrt{7} + 3sqrt{6}`

`= (2sqrt{7} - 2sqrt{7}) + (2sqrt{6} + 3sqrt{6})`

`= 5sqrt{6}`

7) `{2sqrt{3} + 3sqrt{2}}/{sqrt{2} + sqrt{3}} + 1/2cdot(sqrt{2} - sqrt{3})^2`

`= {(2sqrt{3} + 3sqrt{2})cdot(sqrt{2} - sqrt{3})}/{(sqrt{2} + sqrt{3})cdot(sqrt{2} - sqrt{3})} + 1/2cdot[(sqrt{2})^2 - 2cdot sqrt{2}cdot sqrt{3} + (sqrt{3})^2]`

`= {2sqrt{3}cdot(sqrt{2} - sqrt{3}) + 3sqrt{2}cdot(sqrt{2} - sqrt{3})}/{(sqrt{2})^2 - (sqrt{3})^2} + 1/2cdot(2 - 2sqrt{6} + 3)`

`= {2sqrt{6} - 6 + 6 - 3sqrt{6}}/{2 - 3} + 1/2cdot(5 - 2sqrt{6})`

`= {- sqrt{6}}/{-1} + 1/2cdot(5 - 2sqrt{6})`

`= sqrt{6} + 5/2 - sqrt{6}`

`= 5/2 + (sqrt{6} - sqrt{6})`

`= 5/2`

8) Vì đề không rõ ràng nên mình sẽ làm 2 đề, đề nào đúng bạn chép vào nha.

Đề 1: `{3 + 2sqrt{3}}/{sqrt{3}} + {2sqrt{2}}/{sqrt{2} + 1} - (2 + sqrt{3})^2`

`= {(sqrt{3})^2 + 2sqrt{3}}/{sqrt{3}} + {2sqrt{2}cdot(sqrt{2} - 1)}/{(sqrt{2} + 1)cdot(sqrt{2} - 1)} - [2^2 + 2cdot2cdot sqrt{3} + (sqrt{3})^2]`

`= {sqrt{3}cdot(sqrt{3} + 2)}/{sqrt{3}} + {2sqrt{2}cdot sqrt{2} + 2sqrt{2}cdot(- 1)}/{(sqrt{2})^2 - 1^2} - (4 + 4sqrt{3} + 3)`

`= (sqrt{3} + 2) + {4 - 2sqrt{2}}/{2 - 1} - (7 + 4sqrt{3})`

`= (sqrt{3} + 2) + {4 - 2sqrt{2}}/{1} - (7 + 4sqrt{3})`

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

`= sqrt{3} + 2 + 4 - 2sqrt{2} - 7 - 4sqrt{3}`

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

`= - 1 - 2sqrt{2} - 3sqrt{3}`

Đề 2: `{3 + 2sqrt{3}}/{sqrt{3}} + {2sqrt{2}}/{sqrt{2} + 1} - (2 + sqrt{3})` 

`= {(sqrt{3})^2 + 2sqrt{3}}/{sqrt{3}} + {2sqrt{2}cdot(sqrt{2} - 1)}/{(sqrt{2} + 1)cdot(sqrt{2} - 1)} - (2 + sqrt{3})^2`

`= {sqrt{3}cdot(sqrt{3} + 2)}/{sqrt{3}} + {2sqrt{2}cdot sqrt{2} + 2sqrt{2}cdot(- 1)}/{(sqrt{2})^2 - 1^2} - (2 + sqrt{3})`

`= (sqrt{3} + 2) + {4 - 2sqrt{2}}/{2 - 1} - (2 + sqrt{3})` 

`= (sqrt{3} + 2) + {4 - 2sqrt{2}}/{1} - (2 + sqrt{3})` 

`= (sqrt{3} + 2) + (4 - 2sqrt{2}) - (2 + sqrt{3})` 

`= sqrt{3} + 2 + 4 - 2sqrt{2} - 2 - sqrt{3}` 

`= (2 + 4 - 2) - 2sqrt{2} + (sqrt{3} - sqrt{3})` 

`= 4 - 2sqrt{2}`