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A very quick stupid question about square roots of squares

  1. Jun 13, 2012 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution

    If I see an expression like

    [tex]\sqrt{E^2c^2}[/tex]

    I can just remove the square root sign right and replace it with Ec?
     
  2. jcsd
  3. Jun 13, 2012 #2
    Re: A very quick stupid question

    In general, no.

    One must recall that the square root function always returns a positive value. So,
    [tex]\sqrt{X^{2}} = |X|[/tex]
    This is aptly illustrated by [itex]\sqrt{(-1)^{2}} = |-1| = 1[/itex].
    [itex]\sqrt{X^{2}} = X[/itex] iff X is positive.

    (for simplicity, assume that X is always real)
     
  4. Jun 13, 2012 #3
    Re: A very quick stupid question about the square root of a square

    You can't. And please improve the title a bit, like the one you see in the title of this post.
     
  5. Jun 14, 2012 #4
    Re: A very quick stupid question

    In general, you cannot do that. If however, if you know for certain that E and c are both real and positive numbers, then yes you can simplify it to just Ec.
     
  6. Jun 15, 2012 #5
    Re: A very quick stupid question

    help1please,

    I would say yes you can. Once a expression is squared, it loses its signed identity.

    Ratch
     
  7. Jun 15, 2012 #6

    Mark44

    Staff: Mentor

    Re: A very quick stupid question

    That is incorrect. Here's an example why.

    $$ \sqrt{(-4)^2} \neq -4$$

    IOW, if you square a negative number, and then take the square root, you don't get the negative number back.
     
  8. Jun 15, 2012 #7
    Re: A very quick stupid question

    Mark44,

    Correct, that is what I am averring. I am saying it loses its sign identity after it is squared.

    Ratch
     
  9. Jun 15, 2012 #8

    Mark44

    Staff: Mentor

    Re: A very quick stupid question

    That's not what you told the OP.

    So what you are telling the OP is that
    $$ \sqrt{E^2c^2} = Ec$$

    And that is true only if both E and c are nonnegative. If either is negative, the above is not true.
     
  10. Jun 15, 2012 #9
    Re: A very quick stupid question

    Mark44,

    That is exactly what I told the OP. See post #5.

    No, I am saying that √(E^2*C^2) = |E*C|

    Ratch
     
  11. Jun 15, 2012 #10

    Mark44

    Staff: Mentor

    Re: A very quick stupid question

    Yes, I saw post #5, and that is what I'm objecting to.

    The OP's question:

    IOW, help1please is asking if ##\sqrt{E^2c^2} = Ec##

    Your verbatim response in post #5 (again):

    Well, I agree with that, but that isn't what you said before. Your previous response had no mention of absolute values.
     
  12. Jun 15, 2012 #11
    Re: A very quick stupid question

    Mark44,

    OK, you are right. I only half explained it.

    Ratch
     
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