b√(b/a)+a√(a/b)
=b√(ab)/a+a√(ab)/b
=√(ab)(a/b+b/a)
=√(ab)(a^2+b^2)/ab
=√(ab)[(a+b)^2-2ab]/ab
=√(8)[(-8)^2-2*8]/8
=√(8)[64-16]/8
=√(8)*48/8
=6√8
=12√2