1. The problem statement, all variables and given/known data Prove that there exists an x such that x3 = 2 2. Relevant equations 3. The attempt at a solution I have deduced in an earlier part of the question, using the intermediate value theorem, that every monic polynomial of odd degree has a real root. So if I consider x3 - 2 = 0, as a monic polynomial of odd degree, I know that it has a real root. Can I just say that this is the x that I am looking for? I don't feel like I've really proved it fully.