根号7+2分之根号5+2和根号3分之根号2比较大小

（根号n+3-根号n+1）^2=n+3+n+1-2(n+3)(n+1)=-6n-2n^2-2
(根号n+2-根号n )^2=n+2+n-2n(n+2)=2n-2n^2-2
因为-6n-2n^2-2小于2n-2n^2-2 -6n小于2n
所以根号n+3-根号n+1小于根号n+2-根号n