Definition:Binomial (Euclidean)

Definition
Let $a$ and $b$ be two (strictly) positive real numbers such that:
 * $(1): \quad \dfrac a b \notin \Q$
 * $(2): \quad \left({\dfrac a b}\right)^2 \in \Q$

where $\Q$ denotes the set of rational numbers.

Then $a + b$ is a binomial.

Also see

 * Definition:Apotome


 * Binomial is Irrational

Linguistic Note
The term binomial arises from a word meaning two numbers.

This sense of the term is rarely used (if at all) nowadays.