> ... > > 1=1/2*2*v_net^2 > > v_net=0.707

You missed the extra factor of "*2" at the end and took the square root of 1/2 by mistake. Had you taken the square root of "1/2*2" you would have gotten v_net=1, i.e. the speed of the two balls together is the same as each ball separately. But that's because, as other commenters pointed out, you used conservation of energy for a perfectly-elastic collision. Using conservation of momentum in a perfectly-inelastic collision v_net will be zero and all the kinetic energy will be destroyed (converted into thermal energy of the atoms inside the ball bouncing around randomly).