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 number and an irrational numbers is irrational.
(b) The product of a nonzero rational number and an irrational number is irrational.
[Hint: For part (a), suppose that is a rational number , that is, Show that this leads to a contradiction. Use similar reasoning for part (b).]
The sum of rational number r and irrational number t is irrational.
Let us assume that the sum of the irrational number t and rational number r is rational number q.
The difference of two rational number gives a rational number.
This is contradiction to the given t is an irrational number.
Therefore, the must be irrational number
The product of non-zero rational number r and irrational number t is irrational.
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