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Perfect square?

  1. Jan 7, 2008 #1
    "Perfect" square?

    Is a perfect square only "perfect" if the root is a whole number? Or does the term just dictate that decimals must eventually terminate?

    For instance:

    [tex]\displaystyle{\sqrt{59.29} = 7.7}[/tex]
     
  2. jcsd
  3. Jan 7, 2008 #2
  4. Jan 7, 2008 #3

    HallsofIvy

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    A number always has a "decimal expansion". Integers just happen to have all 0s after the decimal point! A "perfect square" is the square of an integer.

    52.29 is NOT a perfect square.
     
    Last edited by a moderator: Jan 7, 2008
  5. Jan 7, 2008 #4
    Though 5229 is a perfect square. If you have a rational number as the result of a root, then the thing inside the root is the square of a rational (in this case, (77/10)^2 = 5229/100), so there are two perfect squares involved somewhere. Other than these musings, all the replies above are, of course, right.
     
  6. Jan 7, 2008 #5

    HallsofIvy

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    My calculator is under the impression that 772= 5929, not 5229.
     
  7. Jan 7, 2008 #6
    Arrgh! Sorry, I just magnified your typo. :D
     
  8. Jan 7, 2008 #7

    HallsofIvy

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    Ooops! The original post does say "59.29", not "52.29" so you were right and I was wrong. I hate when that happens!
     
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