Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.
Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.
The second case illustrates a feature of the recurring continued fraction which represents a complete quadratic surd.
A number of this kind is called a surd; the surd which is the pth root of N is written ¦JN, but if the index is 2 it is usually omitted, so that the square root of N is written, /N.
This e is neither open nor close, but a surd e the pronunciation of which comes very near a.