I'll double-reply, since I think people might also appreciate this... there's a pretty easy way to find the square of 2-leading-digit numbers (and square-roots,

I'll double-reply, since I think people might also appreciate this... there's a pretty easy way to find the square of 2-leading-digit numbers (and square-roots, too.) Direct square: 54^2 = (50 + 4)^2 = 2500 + 2 * 50 * 4 + 4^2. Direct square-root: 3800 = (61^2=3721) + r ~ (61 + (3800-3721)/(2*61) = 61 + 79/122. To check: (61 + 79/122)^2= 3,800.419. You can estimate the "overhead" by noting that 79/122 ~ 2/3 => (2/3)^2 = 0.444. Of course, my grandfather would've just used a slide-rule directly.