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# 1.E: Numbers - Real (ℝ) and Rational (ℚ) (Exercises)

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## Q1

Determine if each of the following is always rational or always irrational. Justify your answers.

1. The sum of two rational numbers.
2. The sum of two irrational numbers.
3. The sum of a rational and an irrational number.

## Q2

Is it possible to have two rational numbers, $$a$$ and $$b$$, such that $$a^b$$ is irrational? If so, display an example of such $$a$$ and $$b$$. If not, prove that it is not possible.

## Q3

Decide if it is possible to have two irrational numbers, $$a$$ and $$b$$, such that $$a^b$$ is rational. Prove it in either case.

1.E: Numbers - Real (ℝ) and Rational (ℚ) (Exercises) is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Eugene Boman and Robert Rogers (OpenSUNY) via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.