Homework Problems Problem 1.10. The fact that that there are irrational numbers a, b such that a' is rational was proved in Problem 1.5. Unfortunately, that proof was non constructive it didn't reveal a specific pair, a, b, with this property. But in fact, it's easy to do this: let a ::= V2 and b::=2 log23. We know 2 is irrational, and obviously ab = 3. Finish the proof that this a, b pair works, by showing that 2 log 3 is irrational. 1.10. GOOD PROOFS IN PRACTICE