Mi loĝas sur la tria etaĝo.

Loĝi means to live / to reside somewhere. So Mi loĝas sur la tria etaĝo means that this is where I live.

If you said Mi estas sur la tria etaĝo, that would mean I am on the third floor right now, without saying that I live there.

So:

• Mi loĝas sur la tria etaĝo = I live on the third floor.
• Mi estas sur la tria etaĝo = I am on the third floor.

Esperanto normally uses sur for floors of a building, just like English says on the third floor.

So:

• sur la tria etaĝo = on the third floor

Using en would sound less natural here, because etaĝo is thought of as a level/surface of a building rather than a container.

A useful contrast:

• Mi loĝas sur la tria etaĝo = I live on the third floor.
• Mi loĝas en apartamento sur la tria etaĝo = I live in an apartment on the third floor.

So you live in the apartment, but on the floor.

Because the third floor is a specific, identifiable floor. In Esperanto, as in English, ordinals often take the definite article when you mean a particular one.

So:

• la tria etaĝo = the third floor

Without la, it would sound more general or less natural in this sentence.

Tria comes from tri (three) plus -a, the adjective ending.

In Esperanto, ordinals are formed this way:

• unu → unua = first
• du → dua = second
• tri → tria = third
• kvar → kvara = fourth

It ends in -a because ordinals behave like adjectives: they describe a noun.

Here, tria describes etaĝo.

Because etaĝo is a noun, and Esperanto nouns end in -o.

So:

• etaĝo = floor/storey
• domo = house
• urbo = city

This is one of the most regular parts of Esperanto grammar:

• nouns end in -o
• adjectives end in -a
• present-tense verbs end in -as

Because -as is the present-tense verb ending in Esperanto.

So:

• loĝas = live / am living
• loĝis = lived
• loĝos = will live
• loĝi = to live

In this sentence, Mi loĝas means I live or I am living.

There is no accusative -n because nothing here is a direct object, and the sentence describes a location, not movement toward a place.

• Mi is the subject.
• sur la tria etaĝo tells where I live.

Compare:

• Mi loĝas sur la tria etaĝo = I live on the third floor.
  
  • location only, so no -n
• Mi iras al la tria etaĝo = I am going to the third floor.
  
  • movement, but shown with al
• Mi iras sur la trian etaĝon = I go onto/up to the third floor.
  
  • directional use with -n

So in your sentence, no -n is needed.

Yes. Esperanto word order is fairly flexible, because the endings show the grammatical roles clearly.

The most neutral order is:

• Mi loĝas sur la tria etaĝo.

But you could also say:

• Sur la tria etaĝo mi loĝas.

That puts more emphasis on sur la tria etaĝo.

Still, for a learner, the original word order is the safest and most natural choice.

It is pronounced roughly eh-TAH-zho.

A few details:

• e = like e in met
• a = like a in father
• ĝ = like the s in measure or the g in genre
• stress in Esperanto usually falls on the second-to-last syllable, so here it is on ta

So: e-TA-ĝo

Not always. This is more about local convention than Esperanto grammar.

In some places:

• third floor means two levels above the ground floor
• in others, it may be counted differently

Esperanto itself does not solve that cultural difference; la tria etaĝo just means the third floor according to the numbering system being used in that context.

So if exact floor numbering matters, context is important.

Yes. Loĝi means to live/reside somewhere, and it does not automatically say whether the situation is permanent forever or just for a period of time.

For example:

• Mi loĝas en Parizo = I live in Paris.
• Mi loĝas ĉi tie dum la somero = I am living here during the summer.

So loĝi is about where someone resides, whether long-term or not.

Because it describes one floor: etaĝo is singular.

In Esperanto, adjectives agree with the nouns they describe in number and case. So:

• la tria etaĝo = the third floor
• la triaj etaĝoj = the third floors

Here there is only one floor being referred to, so tria stays singular.