Dear Mathman,
You said "next week". What calendar are you on? It's been a month and 4 days since you last posted! Come on, your fan can't wait!
Sincerely,
Your Fan
Dear Fan,
Thanks for paying attention. I have no good calendar explanation other than it's been the first prime number shy of the 6th perfect square since I've posted. The perfect square is the perfect vehicle for our next topic anyways: Roots.
Roots are the BFFs of the exponents. I know some may say "BFF"- that's SOOOO 2007 I can't believe you'd use that term Mathman; After all, you are incredibly hip and relevant. Well, most people still know what it means so we're going with it. With me? Groovy.
Let's review exponents: shortcut for repeated multiplication where the base is the number that is repeatedly multiplied and the exponent is the little number high and to the right that tells us how many times we repeatedly multiply.
Ex 4^2 (the ^ means raise that number) = 4x4 = 16. Now you may have heard that 4^2 can be read as "4 squared." NWDTCF? (Now Where Did That Come From) If you remember finding the area of a square, you remember you multiply the side by itself (since they're all the same it doesn't really matter which side you pick). When we get the answer, we measure it in square units (which are tiny squares that fill up the space). Extending this, we get the "Perfect Squares" (made up of squares with side lengths that are counting numbers):
1^2 = 1x1=1
2^2 = 2x2=4
3^2 = 3x3=9
4^2 = 4x4=16
5^2 = 5x5=25
6^2 = 6x6=36
1,4,6,16,25 and 36 are the first Perfect Squares.
Next awesome math term: Square Root. Simply put, that's what the length of the side would be for a square with a given area. Looks like:
___
V
So the easy ones are the square roots of 1,4,9,16,25,36,49,64,81,100 - their square roots are 1,2,3,4,5,6,7,8,9,10 respectively.
Let's tie the whole room together: Pick a positive whole number (no fraction or decimal). Square it (multiply it by itself). Now find the square root of that result. You should get your original number. So the square root is the inverse to ^2.
Take this further: any number raised to a power has a root that "undoes" what it just did. Trying to show this on this blog is next to impossible since I get a "typewriter" interface. And you thought BFF was an old term...
Exponents and Roots - BFFs.
Stay radical (or at least learn a bit more about them)
- Mathman.