Let $\alpha$ be an algebraic number. The degree of $\alpha$ is the degree of the minimal polynomial for $\alpha$ over $\mathbb{Q}$

In a similar manner to polynomials, the degree of $\alpha$ may be denoted $\deg\alpha$

For example, since $x^3-2$ is the minimal polynomial for $\sqrt[3]{2}$ over $\mathbb{Q}$ we have $\deg\sqrt[3]{2}=3$