Câu 1:
`a) 10=4+6=sqrt{16}+sqrt{36}>sqrt{3}+sqrt{2}`
Vậy `10>sqrt{3}+sqrt{2}`
`b) (sqrt{23}+sqrt{25})^2`
`=23+25+2sqrt{23.25}`
`=48+2.sqrt{(24-1)(24+1)}`
`=2.24+2sqrt{24^2-1}`
`<2.24+2.sqrt{24^2}=(2sqrt{24})^2`
`-> sqrt{23}+sqrt{25}<2sqrt{24}`
Câu 2:
`a) sqrt{5+2sqrt{6}}-sqrt{2}`
`=sqrt{3+2sqrt{3}.sqrt{2}+2}-sqrt{2}`
`=sqrt{(sqrt{3}+sqrt{2})^2}-sqrt{2}`
`=sqrt{3}+sqrt{2}-sqrt{2}`
`=sqrt{3}`
