I swear to Cecil I have not been in school for 8 years, so this isn’t a homework question, I just have a personal little project that I’m too dumb for.
How do you figure out the measurement for the side of a square if you know the measurement for the diagonal?

(The square’s gotta fit inside a circle, the points at the corners of the square rest on the circle, so I figure the diagonal of the square is equal to the diameter of the circle- right?)

Actually, you’re correct (as are the others). According to Smeghead (correctly), 2a[sup]2[/sup]=c[sup]2[/sup] (a=side of square, c=diameter of circle). So a=c / sqrt(2). Since c=2r (r=radius), a=2r / sqrt(2) = sqrt(2)r, which was your answer.