Đáp án`+`Giải thích các bước giải:

Ta có:

`M=(sqrt{45+27sqrt{2}}+sqrt{45-27sqrt{2}})/(sqrt{5+3sqrt{2}}-sqrt{5-3sqrt{2}})-(sqrt{3+sqrt{2}}+sqrt{3-sqrt{2}})/(sqrt{3+sqrt{2}}-sqrt{3-sqrt{2}})`

`M=(sqrt{9}*sqrt{5+3sqrt{2}}+sqrt{9}*sqrt{5-3sqrt{2}})/(sqrt{5+3sqrt{2}}-sqrt{5-3sqrt{2}})-((sqrt{3+sqrt{2}}+sqrt{3-sqrt{2}})^2)/((sqrt{3+sqrt{2}}-sqrt{3-sqrt{2}})(sqrt{3+sqrt{2}}+sqrt{3-sqrt{2}}))`

`M=(3(sqrt{5+3sqrt{2}}+sqrt{5-3sqrt{2}})^2)/((sqrt{5+3sqrt{2}}-sqrt{5-3sqrt{2}})(sqrt{5+3sqrt{2}}+sqrt{5-3sqrt{2}}))-(3+sqrt{2}+3-sqrt{2}+2sqrt{(3-sqrt{2})(3+sqrt{2})})/((sqrt{3+sqrt{2}})^2-(sqrt{3-sqrt{2}})^2)`

`M=(3(5+3sqrt{2}+5-3sqrt{2}+2sqrt{(5+3sqrt{2})(5-3sqrt{2})}))/((sqrt{5+3sqrt{2}})^2-(sqrt{5-3sqrt{2}})^2)-(6+2sqrt{3^2-(sqrt{2})^2})/(3+sqrt{2}-(3-sqrt{2}))`

`M=(3(10+2sqrt{5^2-(3sqrt{2})^2}))/(5+3sqrt{2}-(5-3sqrt{2}))-(6+2sqrt{9-2})/(3+sqrt{2}-3+sqrt{2})`

`M=(3(10+2sqrt{25-18}))/(5+3sqrt{2}-5+3sqrt{2})-(6+2sqrt{7})/(2sqrt{2})`

`M=(3(10+2sqrt{7}))/(6sqrt{2})-(18+6sqrt{7})/(6sqrt{2})`

`M=(30+6sqrt{7}-(18+6sqrt{7}))/(6sqrt{2})`

`M=(30+6sqrt{7}-18-6sqrt{7})/(6sqrt{2})`

`M=12/(6sqrt{2})`

`M=(6*2)/(6*sqrt{2})`

`M=2/(sqrt{2})`

`M=(sqrt{2})^2)/(sqrt{2})`

`M=sqrt{2}`

Vậy `M=sqrt{2}`