Adjoined Number/Examples/Root of 2

Example of Adjoined Number

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 $\Q$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): adjoined number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): adjoined number