Going by the Irrational Root Theorem:

Let a and b be rational numbers and let √b be an irrational number.

If a + √v=b is a root of a polynomial equation with rational coefficients then the conjugate a - √b also is a root.

Here's my question:

what if its 3^√3? The conjugate would be -3^√3 would it not? but when put into the equation x^3 - 3 = 0. 3^√3 works but not its conjugate. I don't understand why.