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Math Help - Prove by contradiction

  1. #1
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    Prove by contradiction

    Prove by contradiction that if r is irrational, then r^(1/2) is irrational
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  2. #2
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    Quote Originally Posted by hebby View Post
    Prove by contradiction that if r is irrational, then r^(1/2) is irrational
    Where are you stuck? This is straight fwd
    Hint: If x is rational, what can you say about x^2?
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    well then r^2 is rational as well, eg)4^2 is rational..then what?...thats it?
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    Quote Originally Posted by hebby View Post
    well then r^2 is rational as well, eg)4^2 is rational..then what?...thats it?
    yep !!

    so if sqrt(r) is rational => r is rational (Contradiction !!)
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    Thanks, but we r going the other way around....ie if r is rational then sqrt r is rational.
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    Quote Originally Posted by hebby View Post
    Thanks, but we r going the other way around....ie if r is rational then sqrt r is rational.
    Absolutely not.
    We are saying "if sqrt r is rational then r is rational"
    Plz note the difference carefully
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  7. #7
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    but the questions says if r is irrational then the sqrt r is irrational so we have to work this way right?
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  8. #8
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    Quote Originally Posted by hebby View Post
    but the questions says if r is irrational then the sqrt r is irrational so we have to work this way right?
    dnt confuse yourself. both the statements are equivalent. one implies the other and vice-versa.

    if sqrt r is rational then r is rational (we proved it)
    but r is irrational (as per the question)
    that mean sqrt r can't be rational because otherwise r will be rational (a contradiction)
    hence sqrt r must be irrational !!
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