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
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