However, base words with prefixes and suffixes usually form new words. Another problem involves words with multiple definitions. Are the words "fast" and "set" individual words, or do their many meanings create more words. I would say no, but has one learned a word if one only knows a minority of its uses?
One source claims that the thousand most common words account for 85% of the words used in most conversations. That source came close to saying that that might be enough. However, a casual glance at those thousand words reveals that the list contains the three articles and most of the prepositions, pronouns, and routine conjunctions. While those words are common and very important, they hardly can be said to compose a sufficient vocabulary. Some estimates credit "average" speakers with an active vocabulary of five to ten thousand words (without defining what a word is), and a passive vocabulary of two to three times that many. Without any idea of what the definitions were, that sounds about right to me.