I need to show that a rational + irrational number is irrational. I am trying to do a proof by contradiction.(adsbygoogle = window.adsbygoogle || []).push({});

So far I have:

Suppose a rational, b irrational.

Then a = p/q for p, q in Z.

Then a + b = p/q + b = (p + qb) / q

But I don't know where to go from here because I still have a rational plus an irrational and that is what I am trying to show.

Also, would a similar proof work to show that an irrational + irrational = irrational?

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# Homework Help: Rational and Irrational Numbers

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