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DISCOVER PROVE: Combining Rational and Irrational Numbers
Is rational or irrational? is rational or irrational? Experiment with sums and products of other rational and irrational numbers. prove the following.
(a) The sum of a rational numberĀ r and an irrational numberĀ t is irrational
(b)The product of a rational numberĀ r and an irrational number t is irrational
[Hint: for part (a), suppose that r + t is a rational number q, that is r + t = q. Show that this leads to a contradiction. Use similar reasoning for part (b)]
DISCOVER PROVE:Ā Combining Rational and Irrational Numbers
Is rational or irrational?Is Ā rational or irrational?Ā Experiment with sums and products of other rational and irrational numbers. Prove the following.
(a) The sum of a rational numberĀ r and an irrational numberĀ t is irrationnal
(b)The product of rational numberĀ r and an irrational numberĀ t is irrational
Ā
[Hint: For part (a), suppose that r+t is a rational number q, that is, r+t = q. Show that this leads to a contradiction. Use similar reasoning for part (b)]