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Every root of 2 is irrational.

  1. Jan 15, 2010 #1

    Char. Limit

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    I was thinking on the square root of 2 being irrational proof... and I got the idea that you could use the same idea for every root higher than two. The cube root, the quartic root, the quintic root, etcetera. (Obviously assuming the roots are natural numbers.)

    As a reassurance I'm not crazy, is this correct?
     
  2. jcsd
  3. Jan 15, 2010 #2

    Hurkyl

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    You are not crazy. At least for this particular reason. :wink:
     
  4. Jan 15, 2010 #3

    Char. Limit

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    Good to know.

    Is there a way to prove that other roots that aren't natural numbers are irrational?
     
  5. Jan 15, 2010 #4

    Hurkyl

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    Prime factorization.
     
  6. Jan 15, 2010 #5

    Hurkyl

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    Also, rational root* theorem.

    *: as in, root of a polynomial
     
  7. Jan 15, 2010 #6

    Char. Limit

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    So... are all roots of two that aren't 1 irrational?
     
  8. Jan 15, 2010 #7

    HallsofIvy

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    Almost. Of course the "1" root of 2, 21/1= 2 is rational! If n is a positive integer, greater than 1, then 21/n is irrational.
     
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