Adjoined Number/Examples

Examples of Adjoined Numbers

Adjoining $\sqrt 2$ to $\Q$

Consider the example of a field extension:

Real Numbers of Type $a + b \sqrt 2: a, b \in \Q$

where $\Q \sqbrk {\sqrt 2}$ forms a finite field extension over the rational numbers $\Q$ of degree $2$.

The element $\sqrt 2$ is an example of an adjoined number on $\Q$.