Learn German: Der Schmutz auf dem Boden ist sofort zu entfernen. - The dirt on the floor is to be removed immediately.

This is a special structure using sein + zu + infinitive. It acts as an alternative to the passive voice and expresses that something can or must be done. In this context, it expresses strict necessity: the dirt must be removed immediately.

Could I just use the normal passive voice here, like "Der Schmutz muss sofort entfernt werden"?

Yes, absolutely! Der Schmutz muss sofort entfernt werden means the exact same thing. The sein + zu + infinitive structure used in this sentence is just a more formal, punchy way to give an instruction or state a rule.

Why do we use the dative dem in auf dem Boden instead of the accusative den?

auf is a two-way preposition. We use the dative case here because it answers the question "where?" (wo?) to describe a fixed location. The dirt is already resting on the floor. If we were moving something onto the floor (answering "where to?" or wohin?), we would use the accusative den.

Why does zu entfernen go at the very end of the sentence?

In this grammatical structure, the verb sein (here as ist) acts as the conjugated verb and takes the normal second position in the sentence. The zu + infinitive part gets pushed to the very end, similar to how an infinitive or past participle behaves in a sentence with a modal verb.