Thread: Prove that (√2)^(√2) is irrational (assuming that √2 is irrational).

1. Prove that (√2)^(√2) is irrational (assuming that √2 is irrational).

Prove that (√2)^(√2) is irrational (assuming that √2 is irrational).

2. Originally Posted by feyomi
Prove that (√2)^(√2) is irrational (assuming that √2 is irrational).
Read this: Gelfond's Theorem -- from Wolfram MathWorld