Definition:Apotome/Sixth Apotome

Definition
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers such that $a - b$ is an apotome.

Then $a - b$ is a sixth apotome iff $a \notin \Q$ and $b \not \in \Q$ and $\dfrac {\sqrt {a^2 - b^2}} a \notin \Q$.



Example
When $a = \sqrt 7$ and $b = \sqrt 5$:

Therefore $\sqrt 7 - \sqrt 5$ is a sixth apotome.