Learn Hardcore Danish: Jeg har tre bøger i rummet.

In Jeg har tre bøger i rummet, the room is a specific one that speaker and listener presumably know about, so it takes the definite form rummet (the room).

The books, however, are just “three books” in general, not three specific, previously known books, so they stay indefinite plural: bøger, not bøgerne.

What are all the forms of bog (“book”) and rum (“room”)?

Bog (common gender, “en”-word):

Singular: en bog (a book)
Definite singular: bogen (the book)
Plural: bøger (books)
Definite plural: bøgerne (the books)

Rum (neuter, “et”-word):

Singular: et rum (a room)
Definite singular: rummet (the room)
Plural: rum (rooms)
Definite plural: rummene (the rooms)

So in the sentence you see:

bøger = indefinite plural of bog
rummet = definite singular of rum

Why is the plural of bog “bøger” and not something like “boger”?

Bog → bøger is an irregular plural. Two things happen:

The vowel changes: o → ø
The plural ending -er is added: bog → bøg-er → bøger

There are quite a few Danish nouns that change their vowel in the plural like this (called “umlaut” in German grammar), so you just have to memorize bog / bøger as a pair.

What’s the gender of bog and rum, and how does that affect the sentence?

Bog is common gender (an en-word): en bog, bogen, bøger, bøgerne.
Rum is neuter (an et-word): et rum, rummet, rum, rummene.

Gender itself doesn’t change anything in this exact sentence, because there are no articles shown, but it matters when you add them:

Jeg har en bog i rummet. – I have a book in the room.
Jeg har et rum med tre bøger. – I have a room with three books.

You must use en with bog, and et with rum.

Could I say “i et rum” instead of “i rummet”? What’s the difference?

Yes, you can, but the meaning changes:

Jeg har tre bøger i rummet.
→ I have three books in the room (a specific room known from context).
Jeg har tre bøger i et rum.
→ I have three books in a room (some room, not specified which; it’s just a room somewhere).

So et rum = a room (indefinite), rummet = the room (definite).

Why is the word order Jeg har tre bøger i rummet? Could I move i rummet earlier?

The neutral word order in a simple main clause is:

Subject – Verb – (Object) – Adverbials/Prepositional phrases

So:

Jeg (subject)
har (verb)
tre bøger (object)
i rummet (prepositional phrase showing location)

You can move i rummet to the front if you want to emphasize the location. Then you must use inversion (verb before subject):

I rummet har jeg tre bøger. – In the room, I have three books.

But Jeg har tre bøger i rummet is the most neutral and natural version. Something like Jeg har i rummet tre bøger is grammatically possible but sounds awkward in everyday speech.

How is jeg, har, tre, bøger, and rummet pronounced?

Very rough approximations for an English speaker (Danish has sounds that don’t match perfectly):

jeg ≈ “yai” (IPA roughly [jɑj]).
har ≈ “har” with an open a like “father” ([hɑː]; the r is not strongly pronounced as in English).
tre ≈ “treh”, with a French-like r ([tʁeː]).
bøger ≈ “BUR-uh” with the vowel like French eu in peu ([ˈbøːɐ]).
rummet ≈ “RUM-met”, but with a back Danish r ([ˈʁɔmˀət] roughly).

Spoken quickly, tre bøger i rummet will sound quite blended to English ears; hearing it in audio a few times helps a lot.

Is har here the same verb I see in sentences like “Jeg har læst bogen”?

Yes, it’s the same verb at have (to have).

In Jeg har tre bøger i rummet, har is the main verb meaning “possess”: I have.
In Jeg har læst bogen, har is an auxiliary forming the perfect tense: I have read the book.

Same verb, two different grammatical roles.

Could Danish ever use er (“am”) instead of har (“have”) like in some other languages?

No, not for possession.

For “I have three books”, Danish always uses har:

Jeg har tre bøger.

Er is the verb at være (to be) and is used for identity, state, location, etc.:

Jeg er lærer. – I am a teacher.
Jeg er i rummet. – I am in the room.

You don’t say Jeg er tre bøger or Jeg er tre bøger i rummet.

Why is there no article before tre bøger (no en/et or de)?

With numbers, Danish normally doesn’t use an article:

tre bøger – three books
to rum – two rooms
fem biler – five cars

If you want “the three books”, you normally keep the number and mark definiteness on the noun:

de tre bøger or de tre bøgerne (usage varies; many speakers prefer de tre bøger in normal speech).

But just tre bøger on its own never takes en/et.

Can I omit jeg like in Spanish or Italian and just say “Har tre bøger i rummet”?

No. Danish is not a “pro-drop” language; you normally need to state the subject pronoun:

Correct: Jeg har tre bøger i rummet.
Incorrect / very marked: Har tre bøger i rummet.

Leaving out jeg might be understood in very casual note-taking or in headlines, but in normal speech and writing you should always include jeg.

Why do we use i here and not på? What’s the difference?

Both i and på can translate to “in/on/at”, but their usage differs:

i is used for being inside something:
- i rummet – in the room
- i huset – in the house
- i bilen – in the car
på is used for surfaces and in many set expressions:
- på bordet – on the table
- på skolen – at school
- på arbejde – at work

Since a room is an enclosed space you are in, the natural preposition is i: i rummet.

What part of the sentence is usually stressed?

In neutral speech, you’d normally stress the new or important information, here often the number and the noun:

Jeg har TRE BØger i rummet.

If the fact that they’re in the room is new or contrasted, you might stress that instead:

Jeg har tre bøger i RUMmet (not somewhere else).

The pronoun jeg and the verb har are usually less strongly stressed in a neutral, factual statement.