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LostInParadise's avatar

Can you solve this math problem, which is much simpler than it may at first appear?

Asked by LostInParadise (20985 points ) May 15th, 2014

This is a classic recreational math problem. If you have high school students at home, you may want to share this with them.

We want to show the existence of two irrational numbers a and b such that a^b is rational. To show that two such numbers exist, consider (sqrt(2)^sqrt(2))^sqrt(2)

All you need to know is:
1. (a^b)^c = a^(bc)
2. sqrt(2) is irrational
3. Whole numbers and fractions are rational

Please wait until tomorrow before answering to give others a chance. If nobody answers I will give the solution tomorrow evening.

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