Origin: Latin suffix -al
Irrational has 5 different meanings across 2 categories:
a real number that cannot be expressed as a rational number
"The mathematician spent hours proving that the square root of two is an irrational number because it defies expression as a simple fraction."
A real number that can not be expressed as the quotient of two integers, an irrational number.
"The mathematician spent hours trying to express pi as a simple fraction but realized it was impossible because pi is an irrational number."
Not rational; unfounded or nonsensical.
"His decision to throw away all his savings because he thought aliens were watching him was completely irrational."
The word comes from the Latin irratiōnālis, which combines the prefix ir- with ratiōnālis. It originally meant "not based on reason."