Douglas Harper's Etymology Dictionary
eu-
word-forming element, in modern use meaning "good, well," from comb. form of Greek eus "good," eu "well" (adv.), also "luckily, happily" (opposed to kakos), as a noun, "the right, the good cause," from PIE *(e)su- "good" (cognates: Sanskrit su- "good," Avestan hu- "good"). In compounds the Greek word had more a sense of "greatness, abundance, prosperity," and was opposed to dys-.
Wiktionary
eu-
pre. 1 good, well 2 true, genuine