AMC 8 1987 Problem 19

A calculator has a squaring key $\boxed{x^2}$ which replaces the current number displayed with its 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 $500$? $\text{(A)}\ 4 \text{(B)}\ 5 \text{(C)}\ 8 \text{(D)}\ 9 \text{(E)}\ 250$