Estas necese, ke la paciento ellavu la buŝon per buŝakvo.

Estas necese means It is necessary.

In Esperanto, this kind of impersonal statement is very common:

• Estas necese, ke... = It is necessary that...
• Estas grave, ke... = It is important that...

You can also say Necesas, ke..., which means essentially the same thing.
So these are both good:

• Estas necese, ke la paciento ellavu la buŝon.
• Necesas, ke la paciento ellavu la buŝon.

The version with estas necese is just a little more explicit in structure.

Ke means that and introduces a subordinate clause.

So the structure is:

• Estas necese = It is necessary
• ke la paciento ellavu la buŝon per buŝakvo = that the patient rinse the mouth with mouthwash

In English, that is sometimes optional, but in Esperanto ke is normally expressed clearly in sentences like this.

Ellavu is in the -u form, often called the volitive or jussive form.

After expressions like estas necese, ke..., Esperanto usually uses -u because the action is not simply being described as a fact; it is being presented as something required, desired, intended, or commanded.

So:

• ellavas = rinses / is rinsing
• ellavos = will rinse
• ellavu = should rinse / is to rinse / rinse

In this sentence, ellavu fits because the meaning is something like:

• It is necessary that the patient rinse...
• The patient must rinse...

This is one of the most common uses of -u in subordinate clauses.

Because it is made from:

• el- = out
• lavi = to wash

So:

• el + lavi → ellavi

The two ls are both kept in writing. This is normal in Esperanto when a prefix ends with the same letter that the root begins with.

So ellavu is simply the -u form of ellavi.

Lavi means to wash.
El- often gives the idea of out, outward, or completely out.

So ellavi means something like:

• to rinse out
• to wash out

That is why ellavu la buŝon is more specific than just lavu la buŝon. It suggests rinsing the mouth out, not merely washing it in a general sense.

The -n ending marks the direct object.

Here, the patient is doing the action of rinsing, and the mouth is what is being rinsed:

• la paciento = subject
• ellavu = verb
• la buŝon = direct object

So buŝon gets -n because it receives the action.

Both can be possible, but la buŝon is very natural here.

In Esperanto, when talking about body parts or clothing, the language often uses la rather than a possessive if the owner is obvious from context.

So:

• La paciento ellavu la buŝon
  = The patient should rinse the mouth
  naturally understood as their own mouth

You could say sian buŝon if you want to make the reflexive ownership extra explicit:

• La paciento ellavu sian buŝon

But in ordinary usage, la buŝon is often enough.

Yes, la paciento means the patient—usually a specific patient already known from the situation.

For example, in a medical instruction, the speaker probably means the patient under discussion, not patients in general.

If you wanted a more general meaning like a patient, you could say:

• paciento without la

But in this sentence, la paciento sounds like a particular patient in a particular context.

Per means by means of, using, or with in the sense of an instrument or method.

So:

• per buŝakvo = using mouthwash / with mouthwash

It tells you what is used to perform the action.

This is different from English with, which can mean several things. Esperanto often uses per when something is the tool, means, or substance used.

Examples:

• Mi skribas per krajono. = I write with a pencil.
• Li lavis la manojn per akvo. = He washed his hands with water.

Buŝakvo is a compound word:

• buŝo = mouth
• akvo = water

So buŝakvo literally means mouth-water, i.e. mouthwash.

Compound words are very common in Esperanto. Usually the last part is the main idea, and the earlier part modifies it. So here it is a kind of akvo associated with the buŝo.

Not directly. It is a statement of necessity, not a command spoken straight to the patient.

• Estas necese, ke la paciento ellavu la buŝon...
  = It is necessary that the patient rinse the mouth...

A more direct command would be something like:

• Ellavu la buŝon per buŝakvo! = Rinse your mouth with mouthwash!

So the original sentence sounds more formal, objective, or instructional—something you might read in medical guidance or hear in a professional context.