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Exponent question

  1. May 17, 2005 #1
    [tex] \sqrt x = x^ {.5} [/tex] and [tex] \sqrt [.5] x = x^2 [/tex]

    They are the same but i want to know why.
     
  2. jcsd
  3. May 17, 2005 #2
    Because that's what the radical symbol means: raise the number inside to the reciprocal of the little number of the radical.
     
  4. May 17, 2005 #3

    uart

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    Think of it like this : (x^0.5) (x^0.5) = x^(0.5+0.5) = x^1 = x

    So since (x^0.5) (x^0.5) = x then it follows that x^0.5 must be the square root of x (because when it's multiplied by itself it equals x).
     
    Last edited: May 17, 2005
  5. May 17, 2005 #4
    [tex]\sqrt x = x^5[/tex]
    [tex](\sqrt x)^2 = (x^5)^2[/tex]
    [tex]x = x^{10}[/tex] (notice at this point that x is either 0 or 1)
    [tex](x)^{\frac{1}{5}} = (x^{10})^{\frac{1}{5}}[/tex]
    [tex]\sqrt [5] x = x^2[/tex]
     
  6. May 17, 2005 #5

    dextercioby

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    I doubt that.You left out 8 distinct complex (with nonzero imaginary part) solutions.

    Daniel.
     
  7. May 17, 2005 #6

    shmoe

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    For the life of me I can't remember ever seeing the notation [tex]\sqrt[n]{x} [/tex] where n was anything but a positive integer.
     
  8. May 17, 2005 #7
    But the original poster wrote x^ 0.5 so how did you get to x = x^10 ?
     
  9. May 17, 2005 #8
    the original poster posted .5 not just 5. he wasn't implying
    [tex] \sqrt x= x^5[/tex] he said [tex] \sqrt x= x^{.5} = x^{\frac{1}{2}} [/tex]

    this is true because as jdavel said, the radical symbol means: raise the number inside to the reciprocal of the little number of the radical.

    [tex] \sqrt [2] x= x^{\frac {1}{2}} ; \sqrt [n] x= x^{1/n}[/tex]
    the way you wrote the other equality is a bit odd, but its the same idea...
    [tex] \sqrt [.5] x= \sqrt [\frac {1}{2}] x= x^2 [/tex]
     
  10. May 17, 2005 #9
    ok thanks even though it took me 10mins to understand it all
     
  11. May 17, 2005 #10
    sorry, my screen resolution is such that it looked like a 5, not .5. my apologies for the additional confusion.

    so essentially this "problem" boils down to knowing 0.5 = 1/2? well, duh, if i had realized that i wouldn't have bothered responding.
     
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