Hullet i tanden ligger tæt på tandroden og tandnerven.

Because hullet is the definite form of the noun et hul (a hole).

• et hul = a hole
• hullet = the hole

In this sentence, we are talking about a specific hole, so Danish uses the definite form hullet.

Also note that hul is a neuter noun, so its definite ending is -et.

Because tanden means the tooth, and Danish often uses the definite form when referring to a specific body part in context.

• en tand = a tooth
• tanden = the tooth

So hullet i tanden means the hole in the tooth.

This is very natural in Danish when the speaker has a particular tooth in mind, such as in a dental or medical context.

Because i means in, and a cavity or hole is understood as being inside the tooth, not just on the surface.

• i tanden = in the tooth
• på tanden = on the tooth

So if you are talking about decay or a cavity, i tanden is the natural choice.

Ligger literally means lies or is situated. In Danish, it is very common to use verbs like ligge, stå, and sidde to describe location.

So:

• Hullet ... ligger tæt på ... = The hole is located close to ...

You could sometimes translate it simply as is, but Danish often prefers ligger when talking about where something is physically located.

This is similar to how Danish says:

• Byen ligger ved kysten = The city is on the coast
• Bogen ligger på bordet = The book is on the table

Tæt på means close to or near.

It is a fixed expression:

• tæt = close/tight
• på = on/to, but here it is part of the expression

So:

• ligger tæt på tandroden = is close to the root of the tooth

You should learn tæt på as one unit meaning near.

Because Danish, like English, often forms compound nouns. But Danish usually writes them as one single word.

• tand
  • rod = tandrod = tooth root
• tand
  • nerve = tandnerve = tooth nerve / dental nerve

Then in the definite form:

• tandroden = the tooth root
• tandnerven = the tooth nerve

This is very normal in Danish. English sometimes uses spaces where Danish does not.

Because the sentence refers to specific anatomical parts:

• tandroden = the tooth root
• tandnerven = the tooth nerve

In Danish, it is natural to use the definite form here, especially in medical or dental descriptions.

So tæt på tandroden og tandnerven means close to the tooth root and the tooth nerve.

Here are the nouns and their genders:

• et hul → neuter
• en tand → common gender
• en tandrod → common gender
• en tandnerve → common gender

That is why the definite forms are:

• hullet
• tanden
• tandroden
• tandnerven

A useful pattern:

• common gender definite: -en
• neuter definite: -et

Yes. This is standard Danish word order for a main clause:

• Hullet i tanden = subject
• ligger = verb
• tæt på tandroden og tandnerven = adverbial/prepositional phrase

So the structure is basically:

subject + verb + rest

That makes the sentence straightforward and neutral in tone.

A very natural English translation would be:

• The cavity is close to the root of the tooth and the nerve.
• or The hole in the tooth is close to the root and the nerve.

Danish often sounds a bit more literal if translated word-for-word. For example, ligger tæt på is literally lies close to, but in English we usually say is close to or is located close to.

A rough guide is something like HUL-et, with the stress on the first syllable.

A few points for an English speaker:

• u in hul is not like English u in cut
• the tt in hullet is pronounced as a normal t sound
• the final -et is usually light and unstressed

If you know IPA, it is approximately [ˈhuləð] or [ˈhuləd] depending on pronunciation style, but many learners do best by first remembering the rhythm: HUL-let / HUL-et.

The most important thing is to stress the first syllable.

Sometimes yes, but tæt på is more natural here.

• tæt på = close to
• nær = near

In medical or physical descriptions, tæt på often sounds especially natural when something is very close to something else.

So:

• Hullet i tanden ligger tæt på tandroden og tandnerven sounds very normal.

Using nær would usually sound a bit less idiomatic in this exact sentence.