Definition:Binomial (Euclidean)/Fourth Binomial/Example

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

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

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

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

Then:

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