English word careless comes from Old English carlēas

Detailed word origin of careless

Dictionary entry	Language	Definition
carlēas	Old English (ang)
careles	Middle English (enm)
careless	English (eng)	(archaic) Free from care; unworried, without anxiety. [from 11thc.]. Not concerned or worried (about). [from 11thc.]. Not giving sufficient attention or thought, especially concerning the avoidance of harm or mistakes. [from 16thc.].

Words with the same origin as careless