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Homework Help: Rationalizing the denominator

  1. May 26, 2010 #1

    majormuss

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    1. The problem statement, all variables and given/known data

    I am confused with this equation I found online... It seems wrong to me, I need help.
    My question is,why did the person who worked taht equation use a x^2 to rationalize the equation when the actual equation was an x^3??
    http://tutorial.math.lamar.edu/Classes/Alg/Radicals_files/eq0081MP.gif
    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 26, 2010 #2

    Dick

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    Because the fifth root of x^2*x^3=x^5 is x. How would you do it??
     
  4. May 26, 2010 #3

    majormuss

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    no my question is... why was x^2 used instead of x^3 to rationalize the denominator? my thinking is if x^2 is the denominator then why use x^3 to rationalize it?
     
  5. May 27, 2010 #4

    HallsofIvy

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    Because [itex]x^2*x^3= x^5[/itex] as Dick said. The crucial point is that it is the fifth root that is to be rationalized. You have to multiply what ever power is necessary to get a fifth power inside the fifth root.

    In general to rationalize the denominator of [itex]1/\sqrt[n]{x^m}[/itex] you need to multiply numerator and denominator by [itex]\sqrt[n]{x^{n-m}}[/itex]. That way, in the denominator you will have [itex]\sqrt[n]{x^nx^{n-m}}= \sqrt[n]{x^n}= x[/itex].
     
  6. May 27, 2010 #5

    majormuss

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    I get it now thanks..
     
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