I'm not sure whether this is the correct forum, so I apologise if it's in the incorrect forum. Anyway, when studying A level maths a few years ago, we came across a technique for calculating roots that my teacher claimed was used before calculators were invented. I can't remember the actual technique used, but I remember thinking at the time that it was particularly clever. He also claimed that before calculators, mathematicians were forced to invent other, similarly clever techniques to work out their logs and roots etc. So, what were these techniques? How exactly were the logs and roots calculated before modern computing machines?