evolution - Inbreeding Coefficient and Coefficient of Relationship

Wikipedia gives the following formula to calculate a "path of coefficient of relationship" between an ancestor $A$ and an offspring $O$:

$$\rho_{AO} = 2^{-n} \left( \frac{1+f_A}{1+f_O} \right)^{1/2} = \left( \frac{1}{2}\right)^n \sqrt { \frac{1+f_A}{1+f_O}}$$

, where $f_A$ and $f_O$ are the coefficient of inbreeding of the ancestor and the offspring respectively.

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Question

Where does the term $\sqrt { \frac{1+f_A}{1+f_O}}$ comes from? Please explain why this multiplicative term is $\sqrt { \frac{1+f_A}{1+f_O}}$ and not something different such as $\frac{f_A f_O}{2}$ for example.