Definition:Binomial (Euclidean)/First Binomial

Definition
Let $a$ and $b$ be two positive real numbers, such that $a + b$ is a binomial.

Then $a + b$ is a first binomial iff $a \in \Q$ and $\displaystyle \frac {\sqrt {a^2 - b^2}} a \in \Q$, where $\Q$ denotes the set of all rational numbers.



Example
When $a = 9$ and $b = \sqrt {17}$,

Therefore $9 + \sqrt {17}$ is a first binomial.