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Math Help - Difference between Exponents and Roots

  1. #1
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    Difference between Exponents and Roots

    I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?
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  2. #2
    Site Founder MathGuru's Avatar
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    The Difference is negligable

    Hi Math Buddy, welcome to MHF.

    The truth is that you can represent any root in the form of an exponent

    for example the square root of 2 is also 2 raised to the power of (1/2).

    Or SQRT(2) = 2^(1/2)

    But this may be a more advanced answer for middle school. Does it answer your question?

    Math Guru
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  3. #3
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    Thnk you Math Guru

    The teacher was very impressed with my (actually your) answer. She asked my how I knew that and I told her about your forum.

    Thanks Math Guru,

    Math Buddy
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  4. #4
    Junior Member theprof's Avatar
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    Quote Originally Posted by Math Buddy
    I have a question that asks me to describe what the difference between exponents and roots (if there is any). So what is the difference?
    none, if you trust in fractionals
    Look at this

    in natural numbers (0,1,2,3,4...)
    x^2=4 means x=2, because 2^2=4

    and if I loook for an exponent that gives me

    4^x = 2?

    How much is x?

    not 1 because 4^1 = 4
    not 0 because 4^0 = 1

    something in between, but how much?
    Remember power laws:

    (3^4)^5 = 3^20

    4^x=2 needs that x is... 0.5!
    so 4^(1/2) is the same that sqrt(4), that is 2.

    bye

    hope this helps
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  5. #5
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    I think that the difference between an exponent and a root is that an exponent is a value used as a power to which another value is raised and a root is a number that, when multiplied by itself an appropriate number of times, returns the value under the radical.
    Last edited by tbsmith; June 23rd 2005 at 10:52 PM.
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