Algebra

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I need to rationalize the denominator of 2/3 square root of five, (three being the index). My book suggests you should multiply this by 3 square root of 5^2 over 3 square root of 5^2. I thought the numbers that you rationalize the original with should be the denominator unaltered. Why do you add a ^2 to the 5? Thanks for your help!!!

  • Algebra -

    are you sure this is not

    2
    ____

    5^(1/3)

    ?

    ----------------------
    If that is the case, you need to get 5^1 = 5 on the bottom
    The way to do that is to multiply top and bottom by
    5^(2/3)

    2 * 5^(2/3)
    ______________

    5^(1/3) * 5^(2/3)

    which is

    2 * 5^2/3
    __________
    5

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