Problem 89 of 7
Determine whether sum of two irrational numbers in sqrt(2) + sqrt(8) must be irrational.
Using a hint is okay. It just tells the trainer to give you a little more review.
Hidden until you reveal it.
provide counterexamples.
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Expression must involve two irrational addends or a general claim about them.
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Your answer is equivalent to the expected form.
Walkthrough
Full solution stays hidden until you ask for it.
1. Test the specific irrational addends if given.
2. For a general claim, look for a counterexample such as additive inverses.
3. Conclude that irrational plus irrational is not closed in either direction without more information.
Use the worked steps, then substitute the final answer back into the original relationship to confirm it satisfies the prompt.
Claiming all irrational sums are irrational.