Problem 35 of 7
Determine whether sum 7+sqrt(5) of rational and irrational numbers is irrational.
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reason by contradiction or structure.
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One addend must be rational and one must be irrational.
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Walkthrough
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1. Identify one term as rational and the other as irrational.
2. If the sum were rational, subtracting the rational term would make the irrational term rational.
3. That contradiction shows the sum is irrational.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Assuming irrational plus rational can become rational.