A double star consists of two stars of equal brightness at equal distance from the Earth. What is the apparent magnitude of the combined object?
The magnitude formula is $$m = -2.5 \log_{10} \left(\frac {F}{F_{0}}\right)$$
Where $F_0$ is the flux of magnitude 0 star.
So if you have two stars of equal brightness, the flux is doubled, and you get
$$m = -2.5 \log_{10} \left(\frac {2F}{F_{0}}\right)\\
= -2.5\log_{10}(2) -2.5 \log_{10} \left(\frac {F}{F_{0}}\right)$$
The first value is about -0.75, so the double star is 0.75 magnitudes brighter.  If each object is 8.34 then the double star appears as a 7.59 object.