Square Roots

The idea of a square root is easy if we picked the right numbers, numbers like 4 or 9:

 \sqrt{4} = 2

 \sqrt{9} = 3

When we calculate a square root of a value, we usually get an answer with a decimal it goes and goes and goes and never stops…

 \sqrt{2} = 1.414213562373095048801688...

The above value–I looked it up. However, there is a game we can play:

1 –> 1

1.4 –> 1.96

1.41 –> 1.9881

1.414 –> 1.999396

1.4142 –> 1.99996164

The above is a guessing game where we square the guess to see how close it comes to a value of two.

We can modify this strategy slightly to something a computer can do.

Assume we start with a guess that is too high. We can then take the last digit and drop it by 1 digit. Still to high? Do it again, and keep doing that until you fall below 2 and then keep that number and put a 9 next to it. Repeat the process.

The idea of a fraction goes beyond the math taught in General Math.

An important quantity might be a change of one thing divided by the change to another thing.

A velocity of 60 miles per hour says you can buy a change of 180 miles if you pay for it with a change of time of 3 hours.