As is well-known, some algebraic real numbers can be expressed using radicals, and others cannot; for example, every real number that is a solution to a quadratic, cubic or quartic equation can be expressed using radicals, while solutions to higher-degree equations may not be. Is there a standard convention for what to call this distinction? I have heard the phrases "expressible numbers" and "inexpressible numbers" used orally, but never seen either one in print.
Context: Many of my students are familiar with the distinction between rational and irrational numbers, but unaware that there are "types" of irrational numbers. Ultimately I would like to be able to say
$$\mathbb Q \subset C \subset B \subset \mathbb A \subset \mathbb R$$
where $C$ denotes those real numbers that can be constructed using compass and straightedge, $\mathbb A$ denotes the algebraic real numbers, and $B$ describes the set of real numbers that can be expressed using radicals. I am asking for a single-word description of the latter, in the same way that "constructible" is a concise description of the former.