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Math Help - Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

  1. #1
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    Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

    Hi,

    It took me five minutes to learn latex but finally my question is here.

    x^2 = y
    x = \sqrt{y}
      y^\frac{1}{2}=x

    I am able to imagine  x^2 on the number line in my mind How to imagine something to a power of 1/2 or any fraction on the number line.

    Thank you
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  2. #2
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    Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

    You say "finally my question is here", but I see know question!

    You say "I am able to imagine on the number line in my mind". What do you mean by that? If x= 2 then x^2= 4, a point on the number line, but for general x, x^2 can be any point representing a non-negative number.

    As for sqrt{x}= x^{1/2}, if x= 4 then \sqrt{x}= 2 but, for any non-negative x, \sqrt{x} can, again, be any point representing a non-negative number.
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  3. #3
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    Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

    Hi,


    x^3 = x \times x \times x
    x^\frac{1}{2} = ?? represented in the terms of product of x

    I know this is basics but please provide the imaginative way to represent this
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  4. #4
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    Re: Imagining something to the power of fraction(1/2,1/3,3/4) on the number line

    x^3 = x \times x \times x = y where y >= x >= 1
    x^\frac{1}{n} =  ???  = t then 1 <= t <= x and t to the power of the fraction denominator = x
    example \sqrt{2} = 2^\frac{1}{2} = 1.414^2 \approx 2

    I am still not able to get how the reverse of an operation can be represented in the same form

    multiplication is the reverse of division. Here I see the reverse of exponentiation can be represented using exponentiation itself but the operation is different and its not exponentiation at all

    Exponentiation - Wikipedia, the free encyclopedia.

    nth root - Wikipedia, the free encyclopedia

    In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction:

    \sqrt[n]{x} \,=\, x^{1/n} = why is this ??
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