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Math Help - Square root of a negative number that is squared

  1. #1
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    Square root of a negative number that is squared

    The value of square root of (√(-9)^2) is:

    -9
    9i
    3
    9
    none of these

    which one is the right answer?
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  2. #2
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    i would say the ^2 and the √ cancel each other out leaving -9. But as with every reply i post, im not confident lol

    I just typed it into the calc and it reads 9. So basically, im useless lol
    Last edited by djmccabie; October 29th 2008 at 04:50 PM.
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  3. #3
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    Quote Originally Posted by alaricepent View Post
    The value of square root of (√(-9)^2) is:

    -9
    9i
    3
    9
    none of these

    which one is the right answer?
    So this is what I see:

    (√(-9)^2)

    The square root is over the everything, right? Something like sqrt( (-9)^2)? If so:

    The answer is 9. First you square (-9), then you will have sqrt( 81), which is just 9.

    However, just to clarify, if you have:

    [ √(-9) ]^2, then the answer is just -9 because the square and square root cancels out. I hope that helps.
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  4. #4
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    Quote Originally Posted by alaricepent View Post
    The value of square root of (√(-9)^2) is:

    -9
    9i
    3
    9
    none of these

    which one is the right answer?

    = {\sqrt {(-9)^2}}

    =  {\sqrt {81}}

    ={9}
    Last edited by Shyam; October 29th 2008 at 08:00 PM.
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  5. #5
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    Quote Originally Posted by alaricepent View Post
    The value of square root of (√(-9)^2) is:

    -9
    9i
    3
    9
    none of these

    which one is the right answer?
    (-9)(-9) = 81 since a negative times a negative equals a positive.
    square root(81) technically = -9 and 9, but sinc ethis is in elementary and middle school math section, I'm assuming you're only dealing with positive numbers. So, the answer would be 9
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  6. #6
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    Quote Originally Posted by kathrynmath View Post
    (-9)(-9) = 81 since a negative times a negative equals a positive.
    square root(81) technically = -9 and 9, but sinc ethis is in elementary and middle school math section, I'm assuming you're only dealing with positive numbers. So, the answer would be 9
    No. x^2= 81 for x= 9 or -9 but \sqrt{81}= 9, not -9. The square root of a number is defined as the positive root.
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