Мне нужен точный адрес библиотеки.

Because Russian expresses need differently here.

In English, we say I need..., where I is the subject.
In Russian, нужен / нужна / нужно / нужны works more like:

• to be needed
• to be necessary to someone

So мне нужен точный адрес библиотеки literally feels like:

• To me, the exact address of the library is needed.

That is why Russian uses мне, which is the dative case of я.

• я = I
• мне = to me / for me

This pattern is very common:

• Мне нужен билет. = I need a ticket.
• Ему нужна помощь. = He needs help.
• Нам нужны документы. = We need documents.

Because нужен agrees with the noun адрес.

In this sentence, the thing being needed is адрес, and адрес is:

• masculine
• singular

So the correct form is нужен.

Agreement pattern:

• нужен → masculine singular
• нужна → feminine singular
• нужно → neuter singular
• нужны → plural

Examples:

• Мне нужен адрес. → address is masculine
• Мне нужна карта. → map is feminine
• Мне нужно место. → place/seat is neuter
• Мне нужны билеты. → tickets are plural

Even though точный адрес has two words, the key noun is адрес, so that determines the form.

Точный адрес is in the nominative case.

That may feel surprising to an English speaker, because in English the thing after need looks like a direct object. But in Russian, with нужен, the structure is different.

The person who needs something is in the dative:

• мне

The thing needed is in the nominative:

• точный адрес

So grammatically, адрес behaves like the subject of the expression нужен.

You can think of the structure as:

• [To me] [is needed] [the exact address of the library].

That is why you do not use the accusative here.

Because it means of the library.

The phrase адрес библиотеки literally means:

• the address of the library
• or more naturally in English, the library’s address

Here:

• библиотека = library
• библиотеки = of the library

This is the genitive singular form.

Russian often uses this noun + genitive pattern where English might use of or an apostrophe:

• адрес библиотеки = the library’s address
• дверь дома = the door of the house / the house’s door
• номер телефона = phone number

So библиотеки answers the question address of what? → of the library.

In this sentence, точный most naturally means exact or precise.

So точный адрес suggests:

• the full, correct address
• not just a rough location
• not something vague like near the park

Depending on context, точный can also mean accurate, but with адрес, exact/precise address is the most natural understanding.

Examples:

• Мне нужен точный адрес. = I need the exact address.
• Это не точный ответ. = That is not an accurate answer.
• Укажи точное время. = Specify the exact time.

Yes. Russian word order is more flexible than English word order.

The neutral, natural version is:

• Мне нужен точный адрес библиотеки.

But other orders are possible, especially to change emphasis:

• Точный адрес библиотеки мне нужен.
• Адрес библиотеки мне нужен точный.
  (less neutral, but possible in speech for emphasis)

Usually, the original sentence sounds the most standard and neutral.

A rough guide:

• what comes earlier is often already known or less emphasized
• what comes later can sound more important or contrastive

So:

• Мне нужен точный адрес библиотеки. → neutral statement
• Точный адрес библиотеки мне нужен. → emphasizes that it is the exact address that I need

Not exactly in the same way.

You can say:

• Мне нужен точный адрес библиотеки.
• Мне нужен адрес библиотеки.

But with надо, Russian usually prefers a different structure, often with an infinitive or a clause:

• Мне надо узнать точный адрес библиотеки. = I need to find out the exact address of the library.
• Мне надо, чтобы ты прислал точный адрес библиотеки. = I need you to send the exact address of the library.

A sentence like Мне надо точный адрес библиотеки may be understood in colloquial speech, but it is less standard than мне нужен...

So for learners, the safest choice here is:

• Мне нужен точный адрес библиотеки.

Yes, sometimes, if the context makes it clear.

You could say:

• Нужен точный адрес библиотеки.

This can mean something like:

• An exact address of the library is needed
• or, in conversation, I need the exact address of the library

Russian often omits words that are understood from context. But including мне makes it explicit that I am the person who needs it.

So:

• Мне нужен точный адрес библиотеки. → clear and complete
• Нужен точный адрес библиотеки. → more context-dependent, a bit more impersonal

You simply add не before нужен:

• Мне не нужен точный адрес библиотеки.

That means:

• I don’t need the exact address of the library.

The structure stays the same:

• мне = to me
• не нужен = is not needed
• точный адрес библиотеки = the exact address of the library

In modern Russian, the noun usually stays in the nominative with не нужен:

• Мне не нужен билет.
• Мне не нужна помощь.
• Мне не нужны деньги.

The stress is:

• Мне́ ну́жен то́чный а́дрес библиоте́ки.

Word by word:

• мне → stressed, but short
• нужен → stress on the first syllable: ну́жен
• точный → stress on the first syllable: то́чный
• адрес → stress on the first syllable: а́дрес
• библиотеки → stress on те́: библиоте́ки

A rough pronunciation guide:

• mne NOO-zhen TOCH-ny A-dres beeb-lee-a-TYE-kee

A couple of notes for English speakers:

• мне begins with a consonant cluster that may feel unusual; try not to insert a vowel before it.
• ы in точный does not sound like English ee. It is a separate Russian vowel sound.
• Russian stress is important and should be learned with each word.

It is the most normal and straightforward way.

Russian commonly uses:

• noun + genitive noun

So:

• адрес библиотеки = the address of the library / the library’s address

Russian does not usually form possession the way English does with ’s. Instead, it often uses the genitive case.

In some contexts, you might also hear an adjective like библиотечный, but библиотечный адрес would not normally mean the same thing here. It would sound more like library-related rather than specifically the address of the library.

So for this meaning, адрес библиотеки is the correct and natural choice.