Thursday, October 25, 2012

60 seconds Good-to-knows - 25 October 2012

Let's review some basic mathematical concepts...  

1. You can't divide by 0.  This mathematical fact has been a favorite of teachers for years.  0 divided by any number is equal to 0 but any number divided by 0 is undefined.  Although there are many ways to show why you can't divide by 0, perhaps this simple, non-rigorous example will suffice: let's divide 3 by 0 and say that the answer is "x" which is representative of some real number.  In other words, 3 / 0 =  x.  If you cross multiply then you get (0) (x) = 3.  In other words 0 = 3, which is clearly false.  Don't worry if you don't understand this example...  All you need to remember is that any number divided by 0 is undefined.

2. The square root of a negative number is an imaginary number.  The square root of -1 is, by definition, equal to "i."  Likewise the square root of -5 is equal to 5i.  Unless you are studying complex (imaginary) numbers, if you get a negative number as the radicand (the number under the square root or cube root symbol), then you have probably done something wrong and should re-check your math.

3.  You can take the cube root of a negative number.  The cube root of -8 is equal to -2.  In fact, when ever the root number is odd (e.g. cubed root, 5th root, 7th root, etc...) you can have a negative number in the radicand.

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