Perfect square?

  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. HallsofIvy

    HallsofIvy 40,229
    Staff Emeritus
    Science Advisor

    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: 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.
     
  5. HallsofIvy

    HallsofIvy 40,229
    Staff Emeritus
    Science Advisor

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

    HallsofIvy 40,229
    Staff Emeritus
    Science Advisor

    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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