Der Preis sinkt um drei Euro.

Because der Preis is the subject of the sentence, and subjects are in the nominative case.

• der Preis = the price
• It is the thing that is doing the action: the price is going down.

You would use den Preis only if Preis were a direct object in the accusative case.

sinkt is the 3rd person singular present tense of sinken, which means to sink, to drop, or to go down.

Here it is used in an everyday economic sense:

• Der Preis sinkt. = The price is falling / going down.

German often uses sinken for things like:

• prices
• temperatures
• numbers
• levels

Because in a normal German main clause, the conjugated verb usually comes in position 2.

So the structure is:

• Der Preis = position 1
• sinkt = position 2
• um drei Euro = the rest of the sentence

This is one of the most important word-order rules in German.

Here, um drei Euro means by three euros.

The preposition um is often used to show the amount of change:

• steigen um ... = to rise by ...
• sinken um ... = to fall by ...

So:

• Der Preis sinkt um drei Euro. = The price falls by three euros.

It tells you how much the price changes, not what the final price is.

In German, after numbers, Euro usually stays the same:

• ein Euro
• zwei Euro
• drei Euro

Unlike English, German does not normally add -s here.

The same happens with many units and currencies in German.

No. Um has several meanings in German, depending on context.

Some common ones are:

• around / at a time: um acht Uhr = at eight o’clock
• around a place: um das Haus = around the house
• by an amount of change: um drei Euro

So in this sentence, um definitely means by.

Yes, that is possible, but it is a bit different in style.

• Der Preis sinkt um drei Euro. = The price drops by three euros.
• Der Preis wird um drei Euro billiger. = The price becomes three euros cheaper.

Both are understandable and natural, but sinkt is often more direct and common when talking about prices in a factual or economic way.

No, sinken is a strong verb.

Its forms are:

• infinitive: sinken
• present: ich sinke, du sinkst, er/sie/es sinkt
• simple past: sank
• past participle: gesunken

So sinkt is just the normal present-tense form for er/sie/es.

Because drei Euro is just the amount of change, not a specific noun phrase like the three euros.

Here, um drei Euro works like an adverbial phrase telling you by how much the price falls.

So German simply says:

• um drei Euro = by three euros

not

• um die drei Euro

unless you mean something different, such as approximately those three euros in a specific context.

No. Der Preis sinkt um drei Euro means the price goes down by three euros.

It does not mean the new price is three euros.

If you wanted to say the new price is three euros, you would say something like:

• Der Preis sinkt auf drei Euro. = The price falls to three euros.

This is a very important distinction:

• um drei Euro = by three euros
• auf drei Euro = to three euros

Depending on context, natural translations include:

• The price drops by three euros.
• The price falls by three euros.
• The price goes down by three euros.

All of these match the German sentence well.

A rough English approximation is zinkt, but with a short i sound.

A few details:

• s at the beginning of a word before a vowel is often pronounced like z
• i is short here
• nk is pronounced clearly
• t is also pronounced

So sinkt sounds roughly like zinkt.

Yes, you can, and it is grammatically correct.

If you put Um drei Euro first, the verb still has to stay in position 2:

• Um drei Euro sinkt der Preis.

This version puts more emphasis on the amount of change.

German allows this kind of flexibility, but the verb-second rule still applies.