iracionāls

Via some other European language, ultimately from Latin irratiōnālis, from ir- + ratiōnālis.

The sense "radical; involving mathematical roots" is perhaps related to the fact that the square roots of most integers are irrational.

iracionāls (definite iracionālais, comparative iracionālāks, superlative visiracionālākais, adverb iracionāli)

1. irrational (not understandable by the mind, not rational, not reasonable)

   iracionāls sapnis ― irrational dream

   iracionāla kaislība ― irrational passion

   iracionāls lēmums ― irrational decision

2. (mathematics) irrational (not reducible to a fraction, and integer, or zero)

   iracionāls skaitlis ― irrational number

3. (mathematics) radical (involving mathematical roots)

   izteiksmes, kas satur saknes (daļveida kāpinātājus) sauc par iracionālām izteiksmēm ― expressions that contain roots (fractional exponents) are called radical expressions

   vienādojumu, kas satur sakni (radikāli) ar mainīgo zem tās, sauc par iracionālu vienādojumu ― an equation that contains a root (a radical) with a variable underneath it is called a radical equation

Although iracionāls is the main adjective applied to concepts relating to roots, its antonym racionāls is directly used in this context as well, this is because racionāls (syn. daļveida) is the Latvian term for fractional when talking about exponents and a number raised to a fractional power (racionāls kāpinātājs) is just a different notation to represent a root.

• racionāls

• Vitanda Sakse (1998) Algebra 10.-12. klasei, Rīga: Pētergailis, →ISBN, pages 34, 70