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Thread: Prove by contradiction

  1. #1
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    Prove by contradiction

    Prove by contradiction that 2^(1/3) is irrational.

    I made a=2^(1/3).

    a^2= 2^(2/3)

    then 2^(2/3)= M^2 because we assume a is rational
    N^2
    then what do I do
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  2. #2
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    Quote Originally Posted by hebby View Post
    Prove by contradiction that 2^(1/3) is irrational.

    I made a=2^(1/3).

    a^2= 2^(2/3)

    then 2^(2/3)= M^2 because we assume a is rational
    N^2
    then what do I do
    Do you know the proof of $\displaystyle \sqrt(2)$ is irrational?
    Go along same lines.

    Let $\displaystyle 2^{1/3} = p/q$. Where $\displaystyle (p,q)=1$
    Thus $\displaystyle 2q^3=p^3$
    so $\displaystyle 2|p^3 $=> $\displaystyle 2|p $
    Can you complete?
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  3. #3
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    Thanks...I can see the proof now...Merci!..it was quite easy
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