What is the name (there must be one!) for real (or perhaps complex) numbers expressible as radicals? Radical numbers? Solvable numbers? (following the same logic as ‘solvable group’). In other words, fill in the blank: Abel proved that there are algebraic numbers that are not _ numbers.
Just to be definite, I want a word for those real numbers that result from exactly evaluating an expression built out of only the constants 0 and 1, the binary operations of addition, subtraction, multiplication, and division, and the infinite family of unary operations of square root, cube root, etc; forbidding division by 0 or even-index roots of negative numbers (and taking the positive even-index roots of positive numbers). But if you know something similar for complex numbers, then that would be nice too.