You figured out the square root of 520,000 without using a calculator?
Color me impressed.
Numeric approximation
520,000 = 52 * 100²
sqrt(520,000) = sqrt(52) * 100
sqrt(52) will be a bit higher than 7, so the sqrt(520,000) will be a bit higher than 700 (about 721 to be exact)
A bit more work than you'd probably want to do (given that calculator use is pretty much automatic for kiddies these days), but that's how you'd do it without one
That's not too bad.
Color me no longer impressed.