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Math Help - Solving roots

  1. #1
    Newbie
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    Oct 2008
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    Solving roots

    I have a problem here.



    This is a homework were I have to solve the roots and order them from greatest to least. But specifically, my problem is with the roots greater than square. I have no idea how to solve them. I know how to solve square roots, but roots greater than square seem to have different way of solving, and I can't solve them. No idea. Can anyone please help me with these?
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  2. #2
    MHF Contributor
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    For the first series of roots, the square root of 3 is larger than the fifth root of 2, because 3^{(1/2)} > 2^{(1/2)} > 2^{(1/5)}. The tenth root of 5 is larger than the fifth root of 2 because 5^{(1/10)} > 4^{(1/10)} = (2^2)^{(1/10)} = 2^{(1/5)}. Since the square root of 5 is less than 3, we have

    3 > 5^{(1/2)}

    3^{(1/2)} > 5^{(1/4)} > 5^{(1/10)}.

    So the order from smallest to largest is 2^{(1/5)}, 5^{(1/10)}, 3^{(1/2)}.
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  3. #3
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    Thanks

    Thanks a lot for your help!
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