Pre Algebra Roots
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Radical!
Roots

 
 A while back, we talked about a way to write a number times itself. 
 Stuff like:
 

 42

 
 Math people wanted a way to turn this around and say:
 "What number times itself equals 16?"
 
 Math people like to write things as equations, not sentences. 
They make up little codes and use them instead of words. 
 They wanted to write stuff like:
 

 The number that times itself equals 16

 
 in a code that didn't use any words at all.
 What they came up with was a squiggle that goes around the 16.
 It looks like this:
 

 
 It means "The number that times itself equals 16." 
 The squiggle is called a RADICAL.
 
 If we ask: "What is the number that times itself equals 16?" 
 You might think that the answer is 4, because:
 

 4 4 = 16

 
 That's true, but it's not the only answer. 
 Here's another one:
 

- 4 - 4 = 16 

 
 Remember, a negative times a negative also equals a positive!
 
 So:
 

 
 A number that times itself equals say ... 16, 
 is called a "square root" of 16. 
 
 For positive numbers, there will be a positive and a negative square root. 
 The positive number square root is called the PRINCIPAL SQUARE ROOT.
 
 So now we can say:
 

 The square root of 25

 
 or write:
 

 
 or say:
 

 The number that times itself equals 25

 
 They all mean the same thing.
 

 
 When we did exponents, we had problems like:
 

 52 = ?

 
 Now when we have square roots, we have:
 

 ?2 = 25

 
 looks like roots and exponents are related, eh?
 
 When we do exponents, we can have exponents other than 2. 
 We can have exponents like 4 or 27 or any number at all.
 
 We can have the same kind of thing with roots too. 
 We could say:
 
 The number that times itself, and then times itself again equals 27.
 
 The squiggle (radical) for that looks a little different, 
 it's:
 

 
 The little 3 in the squiggle tells us how many times we multiply something 
 to get the number under the radical.
 
 When we need to multiply a number twice, we don't need to write the 2. 
 Any other time, we write the number. 
 So here we need to find a number where:
 

 (the number) (the number) (the number) = 27

 
We could think of this like: 
 

 ?3 = 27

 
 Sometimes we can figure these things out in our heads. 
 Sometimes we can do them with a little work on paper. 
 Most of the time though, we'll want to use a calculator. 
 If your calculator has a key like this on it, 
 you're in business!
 

 

 
 To do our last problem we might punch:
 

 

   copyright 2005 Bruce Kirkpatrick

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