Learn Hardcore Japanese: sizukana heya de nemureru.

静か is a な-adjective (also called an adjectival noun). When you use a な-adjective directly before a noun, you must connect it with な. So you get 静かな部屋 (“a quiet room”).

Why is で used after 部屋 instead of に?

The particle で marks the location where an action takes place. Since 眠れる (“can sleep”) describes an action, you use 部屋で (“in the room”). By contrast, に often indicates a destination or static location (“to/at”), not the place of action.

What is 眠れる? Why isn’t it just 眠る?

眠れる is the potential form of 眠る, meaning “to be able to sleep” or “can sleep.” In Japanese, you change a verb into its potential form to express ability or possibility. For a verb ending in ‑る (like 眠る), the pattern is:

Drop the final る
Add れる
Hence 眠る → 眠れる.

Couldn’t you just say 眠る here?

If you said 静かな部屋で眠る, it would simply mean “sleep in a quiet room” (describing a habitual action or a general statement). By using 眠れる, you emphasize that it’s possible or easy to sleep in a quiet room.

Why is there no subject in the sentence? Who is doing the sleeping?

Japanese often omit the subject if it’s clear from context or if it’s a general statement. Here, it’s implied that “one” or “you” or “I” can sleep in a quiet room. In English we’d supply “you” or “one” even though it’s not in the original.

Why doesn’t the sentence end with だ?

The form 眠れる is already the short (dictionary) form of the potential verb. You only add だ (or です) after nouns or na-adjectives in their plain form (e.g., 静かだ). Verbs in short form don’t take だ.

Is there a difference between 眠れる and 寝られる?

Both can mean “can sleep,” but:

眠れる is the potential of 眠る (to sleep).
寝られる is the potential of 寝る (to lie down/sleep).

Usage notes:

眠れる focuses on falling asleep or the state of being able to sleep.
寝られる is more general (“able to lie down/sleep”) and often feels more colloquial.

In this sentence, 眠れる is perfectly natural when talking about actually falling asleep in a quiet room.