In Longman Dictionary of American English, a sentence reads: "This shows you which are the most important words to know." Shouldn't it read: "This shows you which the most important words are to know?"
Both are valid, as is "This shows you which the most important words to know are" (which is the phrasing you'd be most likely to encounter in speech).
"Which the most important books are to know" is the least "proper" of the three, because the words are the ones it is most important to know, so putting a verb in the middle of that specifier-phrase seems to separate it from its associated noun. To put it another way, the subject of the verb "to be" is "the most important books to know", so splitting that phrase with a verb is not ideal - but it's relatively common nonetheless.