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Another simple square root problem

  1. Dec 15, 2005 #1

    dnt

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    why is the square root of 25 just 5

    but when the question x^2 = 25, the answer becomes +/- 5?

    whats the logic here? i dont quite get it. thanks.
     
  2. jcsd
  3. Dec 15, 2005 #2

    Fermat

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    Square root is a function that returns the positive value only.

    When you have the eqn,

    X² = 25

    then both x=5 and x = -5 are solutions of the eqn,

    Which is why you write down the answer as x = +/- 5

    If you applied the square root function to x², you would get

    Sqrt(x²) = |x|
     
  4. Dec 15, 2005 #3

    dnt

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    so its basically a matter of function vs equation?
     
  5. Dec 15, 2005 #4

    Tom Mattson

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    Solving the equation [itex]x^2=25[/itex] by taking the square root is a bit sloppy, IMO. What you are really doing is a shortcut for the following:

    [itex]x^2-25=0[/itex]

    [itex](x-5)(x+5)=0[/itex]

    [itex]x-5=0[/itex] or [itex]x+5=0[/itex]

    [tex]x=5[/itex] or [itex]x=-5[/itex]

    When you solve the equation by taking the square root (I should say roots), you have to remember that there are two of them.
     
  6. Dec 15, 2005 #5

    Fermat

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    More or less, yes.
     
  7. Dec 16, 2005 #6

    HallsofIvy

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    In general, an equation like x2= a has two solutions.
    One is the square root of a: [itex]\sqrt{a}[/itex].
    The other is the negative of the square root of a:[itex]-\sqrt{a}[/itex].
     
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