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Root(s) of 2-or-more terms

  1. Jun 26, 2010 #1
    Hi, How can I write, for instance, the square root of (a2 + b2) in another form?
    Is there another expression which equals √(a2 + b2), and is it possible for that expression to have its √() holding one term whereas other factors exists outside the √() in that expression...

    Thanks...
     
  2. jcsd
  3. Jun 26, 2010 #2

    Mark44

    Staff: Mentor

    [tex]\sqrt{a^2 + b^2}[/tex]
    can't be further simplified without knowing the values of a and b.

     
  4. Jun 26, 2010 #3
    You can make up something like
    [tex]\sqrt{a^2+b^2}=\sqrt{a^2+\sqrt{a^4-b^4/4}}+\sqrt{a^2-\sqrt{a^4-b^4/4}}[/tex]
    but there is usually no useful simplification.

    Obviously you cannot have
    [tex]\sqrt{a^2+b^2}=f(a)+g(b)[/tex]
    since if you differentiate both sides by a and then by b, then you get zero on the right, but something else on the left.
     
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