The irrational number √2 was discovered by the pythagoreans in Greece in the 5th century BC.  The pythagorean credited with the discovery is Hippasus of Metapontum who was a pythagorean philosopher.  However the Babylonians approximated  √2 on a clay tablet that was dated back to 1700 BC ; using the sexagesimal number system the Babylonians were able to approximate  √2 up to six decimal places.  Another early approximation of  √2 was done in the Sulbasutras, which is an ancient Indian mathematical text.

Sources:

https://en.wikipedia.org/wiki/Square_root_of_2

https://en.wikipedia.org/wiki/Hippasus

https://www.math.utah.edu/~pa/math/q1.html

Babylon and the Square Root of 2