| A while back, we talked about a way to write a number times itself. | ||
| Stuff like: | ||
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42 |
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| 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: | ||
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The number that times itself equals 16 |
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| 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: | ||
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| 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: | ||
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4 × 4 = 16 |
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| That's true, but it's not the only answer. | ||
| Here's another one: | ||
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- 4 × - 4 = 16 |
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| Remember, a negative times a negative also equals a positive! | ||
| So: | ||
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| 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: | ||
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The square root of 25 |
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| or write: | ||
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| or say: | ||
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The number that times itself equals 25 |
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| They all mean the same thing. | ||
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| When we did exponents, we had problems like: | ||
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52 = ? |
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| Now when we have square roots, we have: | ||
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?2 = 25 |
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| 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: | ||
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| 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: | ||
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(the number) × (the number) × (the number) = 27 |
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| We could think of this like: | ||
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?3 = 27 |
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| 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! | ||
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| To do our last problem we might punch: | ||
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copyright 2005 Bruce Kirkpatrick |
