A calculator has a squaring key $\boxed{x^2}$ which replaces the current number displayed with its [square](https://artofproblemsolving.com/wiki/index.php/Perfect_square).  For example, if the display is $\boxed{000003}$ and the $\boxed{x^2}$ key is depressed, then the display becomes $\boxed{000009}$.  If the display reads $\boxed{000002}$, how many times must you depress the $\boxed{x^2}$ key to produce a displayed number greater than $500$?
$\text{(A)}\ 4 \qquad \text{(B)}\ 5 \qquad \text{(C)}\ 8 \qquad \text{(D)}\ 9 \qquad \text{(E)}\ 250$
We just brute force this:
\begin{align*} 2 &\rightarrow 4 \\ &\rightarrow 16 \\ &\rightarrow 256 \\ &\rightarrow 65536>500  \end{align*}
Clearly we need to press the button $4$ times, so $\boxed{\text{A}}$