Learn French: Vous êtes des étudiants intelligents.

Because the rest of the sentence is plural! The noun étudiants (students) shows you are talking to more than one person. If you were using the formal, polite vous with just one student, you would say Vous êtes un étudiant intelligent.

Do I pronounce the 's' at the end of vous?

Normally, the 's' is silent. But because the next word (êtes) starts with a vowel, you connect them. The 's' in vous makes a "z" sound, blending into "voo-zet". This linking of words is called a liaison.

Why is the word des in this sentence? The English translation just says "students".

In English, we usually skip words like "some" when talking about plural nouns. In French, nouns almost always need a little word (an article) in front of them. des is the plural form of un or une, and you cannot drop it here.

Why does intelligents come after étudiants?

In English, adjectives come before the noun ("intelligent students"). In French, the rule is usually the opposite: most adjectives come right after the noun they describe.

Why is there an 's' at the end of intelligents?