Calculating without a Calculator

Ever wonder how your grandparents ever survived math class? No I don't mean it's so hard noone could ever survive, and no math wasn't just really easy "back then". But how would someone do a complex mathematical computation without a calculator.

Yes there were slide rulers, but no, I mean before that. So how would one work out something simple like the square root of 71.

There was of course a much higher reliance on personal math skills, most students these days will use their calculator for simple addition. Oh we've all done it, "just to be sure". So that helped of course, things were much faster. But √71 is still hard. One thing we can do is guess. We know 8^2 is 64 and 9^2 is 81, so √71 is probably 8.4ish. We can then do 8.4^2 which 70.56, not big enough, but not by much, so let's try 8.45^2=71.4025, too big, And so on... It takes a while, and some good long multiplication, but it will work, and you can get as many decimals as you need. So there's the solution.

Let's say every day you and a bunch of people are doing this every day, then maybe we could higher someone to do it for you and do them ahead of time. Then evolved Table books. I picked one of these up a few years back called 6 place tables. Pages and pages of numbers. Want √71, go to the square root chapter, scroll to 71, there's your answer to 6 decimal places.

Now this of course only works for simple math, which for most math classes is enough, but what if you're doing higher level math. Well Roynald Fisher, One of the fathers of statistics, had a solution. He employed 30 women that work as his "Calculator". Monday morning, "Find the √37894.2389. Three people per computation then worked and compared ansers for accuracy.

So the next time you're annoyed with Math, just think about how much mathematical computing power you have in that dollar bin calculator. Anyone before 1900 would give their right arm for it.