What is the difference between 저는 기쁘어요 and 저는 기쁜? According to Google translate, they both mean "I am glad."
저는 기뻐요 means "I am glad". 그쁘어요 should be 기뻐요. 기뻐요 means "is/are glad". In Korean, adjectives already have the meaning "to be/is/are" built into them.
저는 기쁜 is a fragment, not a sentence. 기쁜 means "glad". Not "IS glad". Just "glad". It needs to be followed by a noun. 기쁜 사람 ... " a glad person" (I'm not sure how natural that sounds, but it's just an example)
Both 기뻐요 and 기쁜 come from the dictionary form of the word ... 기쁘다. It means "to be glad"
기쁜 is said to be in its "noun-modifying form". It's the form that is used the way you would think of an adjective being used...coming before a noun (blue hat, fat cat, long hair, fuzzy scarf). It must be followed by a noun, and then that noun followed by a verb or adjective (in the conjugated form) to make sense.
기쁘다 as 기뻐요 is actually said to be a "descriptive verb" not an adjective. It's in that noun-modifying form 기쁜 that its best called an adjective.