Learn German: Unser Schlafzimmer ist klein.

Schlafzimmer is a neuter noun (das Schlafzimmer). Because it is the subject of the sentence (nominative case), the possessive word for "our" takes no extra ending, leaving it as unser. If the noun were feminine or plural, it would be unsere.

How do I know the gender of a long word like Schlafzimmer?

For compound words (words made by sticking two or more words together), the gender always comes from the very last part. Here, the last part is Zimmer (room), which is neuter (das Zimmer). So, the whole word is das Schlafzimmer.

Could Schlafzimmer be plural in this sentence?

No, we know it is exactly one bedroom for two reasons. First, the verb is ist (is), not sind (are). Second, the word for "our" is unser. Because the plural form of Zimmer looks exactly the same as the singular, if it were plural, the sentence would have to be Unsere Schlafzimmer sind klein.

Why doesn't the adjective klein have an ending like kleines?

When an adjective comes after the verb (like ist here) to describe the subject, it does not get an extra letter added to the end. It simply stays in its basic dictionary form. Adjectives only get endings when they are placed directly in front of a noun.