This constant provides an approximate value for the square root of three (`sqrt(3)`).  The `sqrt(3)` is an irrational number. 

Definition of Irrational¹ r

An irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers are those real numbers that cannot be represented as terminating or repeating decimals. As a consequence of Cantor's proof that the real numbers are uncountable and the rationals countable, it follows that almost all real numbers are irrational.^[1]

When the ratio of lengths of two line segments is irrational, the line segments are also described as being incommensurable, meaning they share no measure in common.

Numbers which are irrational include the ratio of a circle's circumference to its diameter ?, Euler's number e, the golden ratio ?, and the square root of two,^[2][3][4] in fact all square roots of natural numbers not being a perfect square are irrational.

Usage

The number 3 was commonplace to us as children. We, at an early age, were able to multiply by three just after learning how to double a number, so it is a little surprising to find that the `sqrt(3)` is something less common: an irrational number.

John Phillip Jones, of MathsEasyAsPie.com, is back with an excellent video proof that `sqrt(3)` is an irrational number.  He uses proof by contradiction to gives a thorough and easy-to-follow proof that the `sqrt(3)` is an irrational number. This video is worth watching for all those entering high school and college mathematics where proof-by-contradiction will enter into your mathematical tool box. 

See Also

Square Root of Two (`sqrt(2)`)

1. ^ http://en.wikipedia.org/wiki/Irrational_number