Question 876540: 2.Explain why the sum of a rational number and an irrational number is irrational.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Assume, on the contrary, that p+q = r where p is rational, q is irrational, r is rational. Then q = r-p. But r-p is rational (due to closure) so q must be rational, contradiction. Therefore the sum of a rational and irrational is irrational.
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