lg5^2+2/3lg8+lg5*lg20+(lg2)^2
=2lg5+2/3lg2^3+lg5*lg(4*5)+(lg2)^2
=2lg5+2lg2+(lg5)^2+lj5*2lg2+)lg2)^2
=2(lg2+lg5)+(lg2+lg5)^2
=2lg10+lg10^2
=2+1
=3