Question

$sqrt{4lg2+ lg^{2}5 }+ sqrt{4lg5+ lg^{2}2 }$

Answer 1

=√(4lg2+(lg10/2)^2) + √(4lg5+(lg10/5)^2)=
=√(4lg2+(lg10-lg2)^2) + √(4lg5+(lg10 -lg5)^2)=
=√(4lg2+1-2lg2+(lg2)^2) + √(4lg5+1-2lg5+(lg5)^2)=
=√(1+2lg2+(lg2)^2) + √(1+2lg5+(lg5)^2)=
=√(1+lg2)^2 + √(1+lg5)^2= |1+lg2|+|1+lg5|=2+lg2+lg5=2+lg2*5=
2+lg10=2+1=3