F(1)=6(1)+2
= 6+2
=8
g(f(1))= 2x/5 +4/5
= 2(8)/5 +4/5
= 16/5 +4/5
= 20/5
=4
The answer would be
m= -25

it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.
factoid: Ancient Greeks were scared of irrational numbers, and they steered clear from √2.