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Thread: proofs

  1. #1
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    proofs

    Use the fact that sqrt2 is irrational to prove that sqrt2 + sqrt3 is irrational

    ...im not sure if I'm posting this right...i dont know how to put the sqrt symbol up. but any help would be much appreciated!!
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  2. #2
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    Quote Originally Posted by amiller3 View Post
    Use the fact that sqrt2 is irrational to prove that sqrt2 + sqrt3 is irrational

    ...im not sure if I'm posting this right...i dont know how to put the sqrt symbol up. but any help would be much appreciated!!
    Suppose that \sqrt{2}+\sqrt{3} is rational, then there exist integers a and b
    such that:

    \sqrt{2}+\sqrt{3}=\frac{a}{b}

    so:

    \sqrt{3}=\frac{a}{b}-\sqrt{2}

    squaring:

    3=\frac{a^2}{b^2}-2\frac{a}{b}\sqrt{2}+2

    from this point it should be simple, so I will leave you to complete the proof
    by contradiction.

    RonL
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