Definition:Binomial (Euclidean)/Second Binomial/Example

Example
Let $a$ and $b$ be two (strictly) positive real numbers such that $a + b$ is a binomial.

By definition, $a + b$ is a second binomial :
 * $(1): \quad b \in \Q$
 * $(2): \quad \dfrac {\sqrt {a^2 - b^2}} a \in \Q$

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

Let $a = 2 \sqrt 3$ and $b = 3$.

Then:

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