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Math Help - Easiest way to solve

  1. #1
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    Easiest way to solve

    What is the easiest way to solve with out a calculator ~ Rank the numbers
    A =2^1/ 3 , B =3^1/ 4 and C =5^1/ 6 from smallest to largest
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  2. #2
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    If 2^(1/3) < 3^(1/4), then

    (2^(1/3))^3 < (3^(1/4))^3

    2 < 3^(3/4)

    2^4 < (3^(3/4))^4

    16 < 3^3

    16 < 27, which is true.

    Therefore 2^(1/3) < 3^(1/4)

    The actual proof requires you to start with 16 < 27 (which is a known true statement) and get to 2^(1/3) < 3^(1/4), but it's essentially the same, just going in reverse order.

    Do the same for the other combinations of numbers you have been given.
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