Can you solve this math problem, which is much simpler than it may at first appear?
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.
This question is in the General Section. Responses must be helpful and on-topic.