What is a suitable name for numbers like $a + b\sqrt{c}$ The motivation for this is to find a succinct name for a data type in a Python module.

Suppose I choose an integer $c$ and I want to talk about the set of numbers of the form $a + b\sqrt{c}$, where $a$ and $b$ are rational numbers. If $c = -1$, for example, then this set is called the set of Gaussian Rationals. Of course, we would usually think only of values of $c$ such that $|c|$ is non-square. If $|c|$ is a square, for example if $c = 4$, then we obtain either the set of rational numbers (if $c$ is nonnegative) or the set of Gaussian Rationals (otherwise).

Suppose, for example, that $c = 2$. What would the set of numbers of the form $a + b\sqrt{2}$ ($a$, $b$ rational) be called?

An obvious generalisation would be to cube and higher roots, for example numbers of the form $a + b \times 2^{1/3} + c \times 2^{2/3}$ where $a$, $b$ and $c$ are rational.
Since $\Bbb Q(\sqrt c)=\{a+b\sqrt c\colon a,b\in \Bbb Q\}$, you could call the elements of this set $\sqrt c\text{-rationals}$.
When c = -1 , we usually call that set as complex numbers.

When c = $\sqrt 2$, we can the set as surds (of type $\sqrt 2$) or simply surds because it is the simplest.