Incommensurable/Examples/6 and Root 3

Example of Incommensurability

$6$ and $\sqrt 3$ are incommensurable.


Proof

From Square Root of Prime is Irrational, $\sqrt 3$ is irrational.

Hence the ratio $6$ to $\sqrt 3$ is irrational.

Hence the result by definition of incommensurable.

$\blacksquare$


Sources

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