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Once upon a time |
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| you might have learned about things called roots. | ||
| Maybe you called it a radical. | ||
| Maybe you just called it a rad. | ||
| Whatever you called it, | ||
| it looked like this ... | ||
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| It doesn't mean much by itself. | ||
| It needs to have something inside of it ... | ||
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| All together, the number and the squiggle means: | ||
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THE NUMBER THAT TIMES ITSELF EQUALS 4 |
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| That is ... | ||
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| Now we just have to figure out | ||
| what number times itself equals 4. | ||
| This one us not too tough. | ||
| Most people know that ... | ||
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2 x 2 = 4 |
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| That means: | ||
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| (At the end of this page, we will talk about another answer to this problem. | ||
| To be completely correct, we should mention this answer now | ||
| Later on in Algebra, we will use this other answer in some problems) | ||
| OK, but what's this got to do with X? | ||
| Thanks, I was hoping that you would ask ... | ||
| What if you have this problem ... | ||
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X2 = 25 |
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| How do you turn this puppy into: | ||
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X = SOMETHING |
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| We can't get there by adding or subtracting anything. | ||
| We can't get there by multiplying or dividing by anything. | ||
| What now? | ||
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| So what we do here, | ||
| is to drop one of those root things onto each side of the = . | ||
| Like this ... | ||
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X2 = 25 |
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| So what have we got? | ||
| What does this mean? | ||
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| It means the number that times itself equals 25. | ||
| So what number times itself equals 25? | ||
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5 × 5 = 25 |
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| So: | ||
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| That makes our problem ... | ||
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| Now lets look at the messy X part. | ||
| What does this mean? | ||
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| It means ... | ||
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THE THING THAT TIMES ITSELF EQUALS X2 |
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| So what times itself equals X 2? | ||
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X × X = X2 |
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| So: | ||
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| That makes our problem ... | ||
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| OK, here's that little detail I mentioned earlier. | ||
| The extra answer you get in these problems | ||
| works like this. | ||
| When we said | ||
| "What times itself equals 4?" | ||
| We gave the answer as 2. | ||
| That's true. But there is another number that times itself equals 4. | ||
| The other answer is -2. | ||
| A negative times a negative is a positive. | ||
| So -2 x -2 = 4 also. | ||
| Later on, we will use this "negative root" in problems. | ||
| For now, we will mostly ignore it. | ||
| The positive root that we will use, | ||
| is most often called the principal square root. | ||
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copyright 2005 Bruce Kirkpatrick |
