Problem 19 (1987 AJHSME)

A calculator has a squaring key $x^2$ which replaces the current number displayed with its square. For example, if the display is $000003$ and the $x^2$ key is depressed, then the display becomes $000009$. If the display reads $000002$, how many times must you depress the $x^2$ key to produce a displayed number greater than $500$?