jmc

Since 56 is a multiple of 4 and 126 is a multiple of 9, we can factor squares out of both terms, getting $\sqrt{(2\sqrt{14})(3\sqrt{14})}=\sqrt{2\cdot 3\cdot 14}$. Then, we can factor $2^2$ out of the outer square root to get $2\sqrt{21}$. Thus $a=2$ and $b=21$, yielding $a+b=\boxed{23}$.