Мне нужно знать точный размер этого стола.

Because Russian often uses an impersonal construction for ideas like I need to...

• мне is the dative case of я
• literally, Мне нужно знать... means something like To me, it is necessary to know...

So Russian does not say this the same way English does. Instead of I need, it often says To me it is necessary.

This pattern is extremely common:

• Мне нужно идти. = I need to go.
• Мне нужно работать. = I need to work.

Нужно means necessary / needed in this kind of sentence.

In Мне нужно знать..., it works as an impersonal predicate, not as a normal adjective agreeing with a noun.

So:

• Мне нужно знать = I need to know
• literally: To me, it is necessary to know

This is why нужно stays in this fixed form here.

A closely related word is надо, which is often interchangeable in everyday speech:

• Мне нужно знать...
• Мне надо знать...

Both mean I need to know...

Because after нужно in this structure, Russian normally uses the infinitive to say what action is necessary.

So the pattern is:

• мне нужно + infinitive

Examples:

• Мне нужно знать. = I need to know.
• Мне нужно купить это. = I need to buy this.
• Мне нужно позвонить. = I need to call.

Here, знать is the action that is necessary.

Because знать is a transitive verb, and its direct object usually goes in the accusative case.

What do I need to know?

• точный размер

For masculine inanimate nouns, the accusative looks the same as the nominative:

• nominative: точный размер
• accusative: точный размер

So even though it looks unchanged, it is functioning as the direct object of знать.

Because Russian expresses the size of this table as:

• размер чего? = size of what?
• этого стола = of this table

So размер is followed by the genitive case when you say what something is the size of.

That is why both words change:

• этот стол = this table
• этого стола = of this table

This is a very common pattern with nouns like:

• цвет дома = the color of the house
• начало фильма = the beginning of the film
• размер комнаты = the size of the room

Because этот стол would mean this table as a standalone noun phrase, but here the meaning is the size of this table.

After размер, Russian needs the genitive:

• размер этого стола = the size of this table

So:

• этот стол = this table
• этого стола = of this table

The demonstrative этот must agree with стол in case, number, and gender, so it also changes to этого.

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

The neutral version is:

• Мне нужно знать точный размер этого стола.

But you could also hear variations like:

• Точный размер этого стола мне нужно знать.
• Мне нужно точный размер этого стола знать.
  (less neutral, more marked)

The original order sounds natural and straightforward. It presents:

1. who has the need: мне
2. what is necessary: нужно знать
3. what must be known: точный размер этого стола

So for learners, the original order is the safest choice.

Yes, and it means almost the same thing, but the structure is different.

• Мне нужно знать точный размер этого стола.
  = I need to know the exact size of this table.

• Мне нужен точный размер этого стола.
  = I need the exact size of this table.

The first sentence focuses on the action of knowing.
The second focuses on needing the information itself.

Also notice the grammar difference:

• нужно = impersonal
• нужен agrees with размер (masculine singular)

That is why it is нужен размер, not нужно размер in that version.

This is a very common aspect question.

• знать = to know
• узнать = to find out / learn

In your sentence, знать means to have the information.

So:

• Мне нужно знать точный размер этого стола.
  = I need to know the exact size of this table.

If you say:

• Мне нужно узнать точный размер этого стола.

that means:

• I need to find out the exact size of this table.

So the difference is:

• знать = possess the knowledge
• узнать = obtain the knowledge

Both can make sense, depending on context.

Yes.

• Мне нужно знать размер этого стола.
  = I need to know the size of this table.

Adding точный makes it more specific:

• точный размер = the exact size

So точный adds emphasis on precision.

Yes, if you mean dimensions rather than just size in a general sense.

• Мне нужно знать точный размер этого стола.
  = I need to know the exact size of this table.

• Мне нужно знать точные размеры этого стола.
  = I need to know the exact dimensions of this table.

The plural version is often used when you mean specific measurements such as:

• length
• width
• height

So in practical situations, точные размеры may even sound more natural.

The stress is:

• мне́
• ну́жно
• зна́ть
• то́чный
• разме́р
• э́того
• стола́

A rough pronunciation guide:

• Мне нужно знать точный размер этого стола.
• mnye NOOZH-na znaht TOCH-ny raaz-MYER EH-ta-va sta-LAH

A few notes:

• мне sounds like mnye
• что / его / этого-type endings often reduce in pronunciation, so этого is pronounced roughly like этава
• final unstressed vowels are reduced in normal speech

It is neutral and perfectly natural.

It works in many contexts:

• shopping for furniture
• asking about shipping
• checking whether a table fits in a room
• discussing design or measurements

It is neither especially formal nor especially casual, so it is a very useful everyday sentence pattern.