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Simplifying a square root

  1. Sep 3, 2009 #1
    1.I can't figure out how the [tex]\sqrt{1+((x^2)/(4-x^2))}[/tex] simplifies to 2 times[tex]\sqrt{1/(4-x^2)}[/tex]


    I have tried rewriting it in different ways, but I can't see how it simplifies. [tex]\sqrt{x^2 + 1/4-x^2}[/tex]
     
  2. jcsd
  3. Sep 3, 2009 #2
    The first thing to do is find a common denominator. Then you will be able to zero out some terms. Then, using the property of a square root, the square root of a fraction is the same as the square root of the numerator over the square root of the denominator. This will give you the answer.
     
  4. Sep 3, 2009 #3
    It may help to rewrite these in a form where you don't need the parentheses.

    [tex]\sqrt{1+{{x^2}\over{4-x^2}}}[/tex] simplifies to [tex]2\sqrt{{{1}\over{4-x^2}}}[/tex]
    Does that make it easier?
     
    Last edited: Sep 3, 2009
  5. Sep 4, 2009 #4
    Hint: 1 in the square root, [tex]1=\frac{4-x^2}{4-x^2}[/tex]
     
  6. Sep 4, 2009 #5

    HallsofIvy

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    In other words, write
    [tex]1+\frac{x^2}{4-x^2}[/tex]
    as
    [tex]\frac{4- x^2}{4- x^2}+ \frac{x^2}{4- x^2}[/tex]
    and add the fractions.
     
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