[a根号下(x+y)]^2-[根号下x+根号下y]^2=
(a^2-1)x+(a^2-1)y-2根号下(xy)>=0
=>(a^2-1)(根号下x-根号下y)^2+[(a^2-1)*2-2]根号下(xy)>=0
=>a^2-1>=0,[(a^2-1)*2-2]>=0
=>a^2>=2
a必须大于0,否则不等式不成立,所以a>=根号2.实数a最小值为根号2.