Definition:Binomial (Euclidean)/Fourth Binomial

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

Then $a + b$ is a fourth binomial iff $a \in \Q$ and $\displaystyle \frac {\sqrt {a^2 - b^2}} a \not \in \Q$.



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

Therefore $3 + \sqrt 2$ is a fourth binomial.