Algebraic Irrational Number/Examples/Root 5
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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