Definition:Binomial (Euclidean)/Second Binomial

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

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



Example
When $a = 2 \sqrt {3}$ and $b = 3$,

Therefore $2 \sqrt {3} + 3$ is a second binomial.