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Math Help - Proving something is irrational

  1. #1
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    Proving something is irrational

    Here's my problem...

    Assume we know that √2 is irrational,

    let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational

    Having a bit of trouble understanding proof and irrationals at uni
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  2. #2
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    Quote Originally Posted by lisa21a View Post
    Here's my problem...

    Assume we know that √2 is irrational,

    let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational

    Having a bit of trouble understanding proof and irrationals at uni
    If x+y\sqrt{2} = r where x,y,r\in \mathbb{Q} then \sqrt{2} = \tfrac{r-x}{y} \in \mathbb{Q}.
    This is impossible.
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