Irrational Number To An Irrational Power = Rational Number?
Have you ever wondered if an irrational number raised to an irrational power could result in a rational number? The answer is, yes it is possible. A classic example to solve this problem is to use the following argument to solve the problem. As we are aware, the square root of 2 is an irrational number. Specifically, square root of 2 is both a real and positive number. Consequently, when we calculate the power of square 2 by itself, the result can be either rational or irrational. If it is a rational number, the problem is resolved, because we got a rational number. If the result is an irrational number, let's calculate the power of square 2 to this number again, then finally we got number 2, which is a rational number. So, either way, we can definitely have a pair of irrational numbers to make the result be rational.
Apart from that, there is an additional example which can satisfy the equation. For example, both log four and square root of 10 are irrational numbers. However, if we calculate the log four power of square root 10, we can finally get a rational number, which can prove the equation.