What is the value of $\displaystyle \sum_{i=0}^{4}1_Q(2^{\frac{i}{2}})$ where $\displaystyle 1_Q(x)$ is the indicator function for the set of rational numbers.
No indeed.
Do you know what an indicator function is? Often it is called a characteristic function.
$\displaystyle I_Q (x) = \left\{ {\begin{array}{rl}
1 & {x \in Q} \\ 0 & {x \notin Q} \\ \end{array} } \right.$