IRRATIONAL & RATIONＮＵＭＢＥＲ。

Consider √2 ^ √2 ,Case 1 :If √2 ^ √2 is a rational number , then the statement is true since √2 is an irrational number.Case 2 :If √2 ^ √2 is an irrational number , then (√2 ^ √2) ^ √2= √2 ^ 2= 2 is rational.Combining 2 cases , even though we donn't know √2 ^ √2 is rational or not ,
we conclude that an irrational number raised to an irrational power can be rational.