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Math Help - negative root?

  1. #1
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    negative root?

    Why is it when you square root a number you get a +/-? Why is it when you solve -4^2 it is -16 and not 16? How can you tell it is +/- for the second question?
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  2. #2
    Senior Member Stroodle's Avatar
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    Hi there

    -4^2=-(4)(4)=-16

    but

    (-4)^2=(-4)(-4)=16

    You get a \pm when you take the square root of a number because both the positive and negative square roots could be the factors: e.g. 4\times4=16 and (-4)\times(-4)=16
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  3. #3
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    So, if it is not in ()'s I assume it is -(4)(4)? Why is it then in some cases it is always -4^2 is always 16?
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  4. #4
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    -(4)^2=-(-4)^2=-16

    (4)^2=16,\ -(4^2)=-16

    (-4)^2=16,\ -(-4)^2=-16

    4(4)=4+4+4+4=16

    -4(4)=-4-4-4-4=-16

    Hence,\ negative\ by\ positive\ means\ successive\ subtraction.

    (-4)(-4)=-[4(-4)]=\ opposite\ of\ subtract\ 4\ four\ times,

    which\ is\ add\ 4\ four\ times.\ Add\ and\ subtract\ are\ opposites.

    This\ is\ why\ negative\ by\ negative\ is\ really\ positive\ by\ positive.

    To\ write\ -4^2\ is\ ambiguous.

    We\ must\ distinguish\ between\ -[(4)^2]\ and\ [(-4)^2]
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  5. #5
    Senior Member Stroodle's Avatar
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    Quote Originally Posted by Barthayn View Post
    So, if it is not in ()'s I assume it is -(4)(4)? Why is it then in some cases it is always -4^2 is always 16?
    In my studies -4^2 has always been taken to equal -16. Maybe sometimes people get lazy and leave out the parentheses, or don't see a distinction between the two...
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