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