Aus dem Kühlschrank brauchst du nur die Milch und die Eier rauszunehmen; den Rest können wir später holen.

Because German often puts a different element in the first position for emphasis or topic.

In a main clause, the finite verb still has to stay in second position. So:

• Aus dem Kühlschrank = first position
• brauchst = second position
• du = then comes after the verb

So the structure is:

• Aus dem Kühlschrank | brauchst | du | ...

This is a very normal German word order pattern. Starting with Aus dem Kühlschrank highlights where the items should be taken from.

The sentence could also be:

• Du brauchst nur die Milch und die Eier aus dem Kühlschrank rauszunehmen.

That is also grammatical, but it puts less emphasis on the fridge.

Because aus is a preposition that takes the dative case.

So:

• der Kühlschrank = nominative
• dem Kühlschrank = dative

That is why you get:

• aus dem Kühlschrank = out of the fridge

Even though English uses of in out of the fridge, German uses the preposition aus, and aus always requires dative.

Here brauchen means to need in the sense of all you need to do is ...

So:

• Du brauchst nur die Milch und die Eier rauszunehmen. = You only need to take out the milk and the eggs.

This use of brauchen + zu + infinitive is very common.

In this sentence:

• brauchst = finite verb
• zu nehmen is part of the infinitive construction
• because rausnehmen is separable, it becomes rauszunehmen

A very literal breakdown is:

• You need only [to take out the milk and the eggs].

Because German puts the infinitive clause at the end in constructions like brauchen + zu + infinitive.

The full infinitive here is based on the separable verb rausnehmen:

• base verb: rausnehmen
• with zu: rauszunehmen

So the sentence works like this:

• brauchst du nur die Milch und die Eier rauszunehmen

German often saves the infinitive part until the end, especially after verbs like:

• brauchen
• versuchen
• anfangen
• vergessen

Because with separable verbs, zu goes between the prefix and the main verb stem.

So:

• rausnehmen → rauszunehmen
• anziehen → anzuziehen
• aufmachen → aufzumachen

This is a standard rule in German.

So zu rausnehmen is incorrect. The correct form is:

• rauszunehmen

Rausnehmen is a common spoken or everyday form of herausnehmen.

Both mean:

• to take out

So:

• die Milch aus dem Kühlschrank rausnehmen
• die Milch aus dem Kühlschrank herausnehmen

Both are understood. In everyday conversation, rausnehmen is very common and sounds natural.

Very roughly:

• herausnehmen can sound a bit more neutral or formal
• rausnehmen is more colloquial

They are the direct objects of rauszunehmen, so they are in the accusative case.

In this sentence, the forms happen to look the same as nominative:

• die Milch = nominative or accusative
• die Eier = nominative or accusative plural

So there is no visible change here, but grammatically they are accusative because they are the things being taken out.

Here nur means only, and it limits what needs to be taken out.

So the idea is:

• You only need to take out the milk and the eggs
• not everything else in the fridge

In this sentence, nur is understood to apply to the noun phrase:

• die Milch und die Eier

So it means:

• only the milk and the eggs

German word order with nur can vary a bit depending on emphasis, but this placement is very natural.

Because den Rest is the direct object of holen, so it is in the accusative case.

The noun is:

• der Rest = the rest

In the accusative, masculine der changes to den:

• nominative: der Rest
• accusative: den Rest

So:

• den Rest können wir später holen = we can get the rest later

Both are possible.

The version in the sentence starts with den Rest to emphasize it:

• Den Rest können wir später holen. = The rest, we can get later.

This is another example of the first position in a main clause being used for emphasis or topic. Once den Rest takes first position, the finite verb must still stay second:

• den Rest | können | wir | später holen

The more neutral version would be:

• Wir können den Rest später holen.

Because können is a modal verb.

After a modal verb, German normally uses a bare infinitive without zu:

• wir können holen
• du musst gehen
• sie will essen

So:

• den Rest können wir später holen

is correct.

By contrast, the first clause uses brauchen + zu + infinitive, so there you do need zu:

• brauchst du ... rauszunehmen

They are similar, but not identical.

• rausnehmen = to take out
• holen = to fetch / get

In the first clause, the focus is specifically on removing items from the fridge:

• die Milch und die Eier rauszunehmen

In the second clause, holen is broader:

• den Rest können wir später holen = we can get/fetch the rest later

That could mean getting the remaining items later, without focusing so much on the physical action of taking them out.

The semicolon links two closely related independent clauses:

• Aus dem Kühlschrank brauchst du nur die Milch und die Eier rauszunehmen
• den Rest können wir später holen

A semicolon is stronger than a comma but softer than a full stop. It shows that the two thoughts belong closely together.

A full stop would also work:

• Aus dem Kühlschrank brauchst du nur die Milch und die Eier rauszunehmen. Den Rest können wir später holen.

That would sound slightly more separated.

Yes, it is natural and understandable.

A few close variants are also very common, for example:

• Aus dem Kühlschrank brauchst du nur die Milch und die Eier rauszunehmen. Den Rest können wir später holen.
• Du brauchst aus dem Kühlschrank nur die Milch und die Eier rauszunehmen; den Rest können wir später holen.
• Du musst aus dem Kühlschrank nur die Milch und die Eier rausnehmen; den Rest holen wir später.

The original sentence sounds fine, especially in everyday spoken German.