√[lg^2(1/3)-4lg3+4] +lg6-lg0.02
=√[lg^2(3)-4lg3+4] +lg6-lg0.02
=√[lg(3)-2]^2+lg6-lg0.02
=2-lg3+lg6-lg0.02
=2+lg(6÷3÷0.02)
=2+lg100
=2+2
=4