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Math Help - Negative roots

  1. #1
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    Negative roots

    I have a little question concerning negative roots. I just happened to be doing an exercise which required taking the fifth root of (-32). I thought that one cannot take a root out of a negative number if the answer is supposed to belong to the real numbers. However is it so one cannot take the square root of a negative number, and any other even root(e.g fourth root, sixth root), but one can take roots of negative numbers if the root is negative(e.g cube root)?
    Last edited by Coach; September 23rd 2007 at 08:40 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Coach View Post
    I have a little question concerning negative roots. I just happened to be doing an exercise which required taking the fifth root of (-32). I thought that one cannot take a root out of a negative number if the answer is supposed to belong to the real numbers. However is it so one cannot take the square root of a negative number, and any other even root(e.g fourth root, sixth root), but one can take roots of negative numbers if the root is negative8e.g cube root)?
    The only difficulty is that we can't take even roots of negative numbers. Odd roots work out just fine because
    (-1)^n = -1
    when n is odd. So you just do this for convenience:
    \sqrt[5]{-32} = -\sqrt[5]{32} = -2

    -Dan
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  3. #3
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    roots and exponents

    I am just learning and was under the impression
    \sqrt[4]{-32} = -32^1/4

    the first equation doesn't seem to work but the second one does.
    can anyone explain to me why.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by xcess View Post
    I am just learning and was under the impression
    \sqrt[4]{-32} = -32^1/4

    the first equation doesn't seem to work but the second one does.
    can anyone explain to me why.
    that's because they are two different things. they are not equal.

    on the left you have (-32)^{1/4} while on the right you have -32^{1/4}. they are not the same thing. the first is not a real number, the second is a negative number

    watch your parentheses. do you understand the difference between the two?
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  5. #5
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    k what is -3 cubed? it is negative right?
    but what is a negative squared, it will never be negative. That is why.
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by harnar View Post
    k what is -3 cubed? it is negative right?
    but what is a negative squared, it will never be negative. That is why.
    Please quote what you are replying to, otherwise your post is just floating and makes little to no sense.

    CB
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