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Math Help - Determine largest number:

  1. #1
    Member great_math's Avatar
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    Determine largest number:

    \ 1,\sqrt{2},\sqrt[3]{3}.....,\sqrt[n]{n}

    Determine the largest number in the above sequence
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  2. #2
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    Quote Originally Posted by great_math View Post
    \ 1,\sqrt{2},\sqrt[3]{3}.....,\sqrt[n]{n}

    Determine the largest number in the above sequence
    The function y = x^{1/x} has a maximum turning point at x = e. Since 2 < e < 3, the question now becomes a simpler one:

    "Which is bigger, \sqrt{2} or \sqrt[3]{3} " .... Which is more or less the same as asking "Which is bigger, (\sqrt{2})^6 or (\sqrt[3]{3})^6 " ....

    Alternatively, note that \sqrt{2} has the same value as \sqrt[4]{4} = 4^{1/4} .....
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