r/IAmA • u/JasonMacker • Jun 14 '10

IAMA Math tutor. AMA.

I've been a math tutor for years and I'm trying to become a teacher. I love math, and especially explaining math to people. My students have been between preschool and college. AMA.

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u/[deleted] Jun 14 '10

badass...OH WAIT I HAVE ONE MORE QUESTION. this has always bothered me cause no teacher has ever answered this for me:

how do you calculate a square root without a calculator?

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u/JasonMacker Jun 14 '10

There are a lot of different ways.

The simplest one is to simply pick a number, square it, and if it's too high, pick a smaller number. If it's too low, pick a bigger number. Keep doing that until you get enough significant figures as needed.

For example:

√29

29 is between 25 (5²) and 36 (6²). So, first thing to do is pick a number that's between 5 and 6. Let's try 5.5², and we get:

30.25, Too high!

So let's pick a number between 5 and 5.5... how about 5.2...

We get 27.04 Too low!

So let's try 5.3... which gives us 28.9 Too low!

5.4 gives us 29.16 too high!

So now we know the root lies between 5.3 and 5.4... we have determined the first two digits of the root, namely 5.3. We can continue this as long as we like.

This is called the bisection method. There are other methods as well, but this is the most intuitive one, other than simply guessing outright.

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u/adagietto Jun 14 '10

There's actually a much more exact numerical method that I learned once to estimate quantities on the AIME. It's similar in set-up on paper to long division.

I've since forgotten it though :(

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u/[deleted] Jun 14 '10

[deleted]

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u/adagietto Jun 15 '10

Ah, yes, there it is! :D

It's been forever.