SOLUTION: √3 - √1/3 answer is 2√3 ___ 3 I need to know how to get the answer.

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Question 93035: √3 - √1/3



answer is 2√3
___
3

I need to know how to get the answer.

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Here's one way of doing the problem:
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Given:
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sqrt%283%29+-+sqrt%281%2F3%29
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Change the second term into the square root of the numerator over the square root of the
denominator to make the given expression become:
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sqrt%283%29+-+sqrt%281%29%2Fsqrt%283%29
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Put the first term over a common denominator of sqrt%283%29 by multiplying the first term
by sqrt%283%29%2Fsqrt%283%29. Since the denominator and numerator of this multiplier are equal,
this is equivalent to multiplying the first term by 1. This multiplication makes the
expression become:
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%28sqrt%283%29%2Asqrt%283%29%2Fsqrt%283%29%29-+%28sqrt%281%29%2Fsqrt%283%29%29
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Notice that the numerator of the first term is sqrt%283%29%2Asqrt%283%29. Multiplying
out the two square roots just results in an answer of 3. And the numerator of the
second term is the square root of 1. But the square root of 1 is just 1. Making these two
changes to the expression results in it becoming:
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3%2Fsqrt%283%29+-+1%2Fsqrt%283%29
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Since both terms have a common denominator the two numerators can be combined over that
common denominator and the result is:
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+%283+-+1%29%2Fsqrt%283%29
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Do the subtraction in the numerator and the expression further simplifies to:
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+2%2Fsqrt%283%29
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Finally, by convention we do not leave a square root in the denominator. To get rid of it,
just multiply the expression by sqrt%283%29%2Fsqrt%283%29 and it transforms the expression:
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And that's the answer you were looking for.
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Hope this helps clarify the problem for you.
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