Why was an irrational number called a 'surd' as opposed to an 'irrat'?

Answer 1

The term surd traces back to al-Khwārizmī, who referred to rational and Irrational Numbers as audible and inaudible, respectively. This later led to the Arabic word "أصم‎" (asamm, meaning "deaf" or "dumb") for irrational number being translated into Latin as "surdus" (meaning "deaf" or "mute").

Answer 2

Only some - a minority - of irrational numbers are called surds. Most of them, such as pi, phi, e are not surds.

Irrational numbers are not rational. They were thought to be "roots that were deaf to reason". The Latin word surdus, (= deaf) led to the term surd.