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Homework Help: Can someone show me how this would turn out

  1. Feb 13, 2007 #1
    What would this number be?
    [tex](3\frac{1}{3})^{\frac{1}{2}}[/tex]
    Is it rational or irational?

    How do you work it out?

    [tex]\frac{10}{3}^\frac{1}{2}[/tex]
     
  2. jcsd
  3. Feb 13, 2007 #2

    cristo

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    Your answer should be [tex]\left(\frac{10}{3}\right)^{\frac{1}{2}}[/tex]

    Do you think it is rational or irrational?
     
  4. Feb 13, 2007 #3
    I THINK it's irrational, because it look ugly. Isn't it [tex]2\sqrt{\frac{10}{3}}[/tex]

    As you put the denominator as the surd outside thingy (wot ever it's called) and the rest inside the root. On a calculator it gives me 2.108185... which is a real number, and virtually all real numbers are irrational?

    P.S How do i tell on a calculator if the number is real or not. It could stop after 50 places, and my calculator only goes to 11
     
  5. Feb 13, 2007 #4

    HallsofIvy

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    You can't. ALL numbers a calculator deals with are rational and so, in general, only approximately the number you want.
     
  6. Feb 14, 2007 #5

    HallsofIvy

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    In general, if a rational number is not the ratio of two perfect squares, i.e. m2/n2, then its square root is not rational.
     
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