Wouldn't it be like a factor of two? Since KP= (theta)/(1-theta) Then the dissociation process needs two surface sites so in a pure system then KP/2 = (theta)/(1-theta). Plugging that into the competitive adsorption isotherm then the denominator would be something like 1 +KP(a) + (KP(b)/2)
If it's not like that then doesn't it depend on the value of K? So I don't think it would be as simple as square the KP(b). Like what if the dissociation reagent binds suuuupper slowly (the equilibrium constant is less than that of the adsorbant you want), so even though it takes up two surface sites it might be negligible compared to the actual adsorbant you want.
In general poisons have really high K values so then I don't think it would be just square the dissociation reagent terms, but it would depend on the value of K.
Dunno if that helps but the TL;DR is that I don't think it's just square root, but it depends on the value of K more than anything.
Edit: formatting and added stuff