In the sentence "Los estudiantes son muy _____," using the word "trabajadores" makes sense because it is an adjective that describes a quality of the students (in this case, 'hard-working'). The word "trabajadores" is the plural form of "trabajador," which means 'worker' or 'hard-working person.' Since "estudiantes" (students) is a plural noun, the adjective needs to agree in number and gender.
"Trabajador" would be singular and would not agree with "estudiantes," leading to a grammatical mismatch. Therefore, the correct form to fill in the blank is "trabajadores" to maintain agreement: "Los estudiantes son muy trabajadores" (The students are very hard-working).