7-4√3=2^2-2*2*√3+(√3)^2=(2-√3)^2

6-4√2=2^2-2*2*√2+(√2)^2=(2-√2)^2

∴√(5-2√6)+√(7-4√3)+√(6-4√2)

=√(√3-√2)^2+√(2-√3)^2+√(2-√2)^2

=√3-√2+2-√3+2-√2

=0