lg5^2+2\3lg8+lg5lg20+(lg2)^2
=2lg5+2/3×3lg2+lg5×（lg5+lg4）+(lg2)^2
=2×(lg2+lg5)+（lg5）^2+2lg5lg2+(lg2)^2
=2lg10+（lg5+lg2）^2
=2+（lg10）^2
=2+1
=3