Definition:Apotome/Sixth Apotome

Definition
Let $a$ and $b$ be two positive real numbers, such that $a - b$ is an apotome.

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



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

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