Algebraic Irrational Number/Examples/Root 5

Example of Algebraic Irrational Number

The number $\sqrt 5$ is an example of an algebraic irrational number.

Proof

We have that $\sqrt 5$ is the root of the polynomial equation $x^2 - 5 = 0$.

Hence by definition $\sqrt 5$ is an algebraic number.

From Square Root of Prime is Irrational, $\sqrt 5$ is also irrational.

Hence the result, by definition of algebraic irrational number.

$\blacksquare$

Sources

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