Mater puero persuadet ut aquam puram bibat.

Mater is in the nominative singular, so it is the subject of the sentence.

A learner might expect a feminine subject noun to end in -a, but mater belongs to the third declension, not the first. Its basic form is already mater, and that nominative form means mother.

So:

• mater = mother as the subject
• persuadet = persuades
• therefore mater persuadet = the mother persuades

Because the verb persuadeo, persuadere works differently in Latin than persuade does in English.

In Latin, persuadeo usually takes:

• the person persuaded in the dative
• the thing/action persuaded in an ut + subjunctive clause

So:

• puero = to the boy / the boy in the sense of the person being influenced
• not a direct object in the accusative

This is a very common pattern:

• alicui persuadere ut... = to persuade someone to...

After persuadeo, Classical Latin normally uses an ut-clause with the subjunctive, not a simple infinitive.

So Latin says:

• puero persuadet ut aquam puram bibat

rather than something like:

• puero persuadet aquam puram bibere

The pattern is:

• persuadeo + dative person + ut + subjunctive

English uses to drink, but Latin expresses that idea with ut ... bibat.

Because ut after a verb like persuadet introduces a clause of what someone is being urged, persuaded, or influenced to do. In Latin, that kind of clause uses the subjunctive.

So bibat is subjunctive because it is not just a plain statement he drinks, but part of the idea:

• she persuades him that he should drink
• more naturally in English, she persuades him to drink

This is one of the standard uses of the subjunctive after verbs of influencing, urging, asking, ordering, and persuading.

Because the main verb persuadet is in a primary tense: the present.

In Latin sequence of tenses, a main verb in a primary tense is usually followed by the present subjunctive for action that is simultaneous or future relative to the main verb.

So:

• persuadet = present
• therefore bibat = present subjunctive

If the main verb were in a past tense, you would normally expect the imperfect subjunctive instead:

• Mater puero persuasit ut aquam puram biberet.
• The mother persuaded the boy to drink pure water.

Because aquam is the direct object of bibat:

• bibat = may drink / drink
• aquam = water

The adjective puram has to agree with aquam in:

• gender: feminine
• number: singular
• case: accusative

So:

• aquam = water
• puram = pure
• aquam puram = pure water

Latin adjectives must match the nouns they describe.

Yes. Latin word order is much more flexible than English word order.

So all of these are possible in Latin, though they may sound slightly different in emphasis:

• aquam puram
• puram aquam

Both mean pure water.

In the sentence you were given, aquam puram is a very natural order. Often an adjective follows the noun, but Latin can place it before or after depending on style and emphasis.

Here ut introduces the clause that completes the idea of persuadet.

In very literal English, you might think of it as:

• that
• or so that he may

But in smoother English, the whole phrase is usually translated with to:

• persuades the boy to drink pure water

So in this sentence, ut is not best understood as a simple standalone word with one fixed English equivalent. Instead, it is part of the construction:

• persuadet ut bibat = persuades ... to drink

Not as important as it would be in English, because the endings show the grammatical roles.

In this sentence:

• mater is nominative, so it is the subject
• puero is dative, so it is the person persuaded
• aquam puram is accusative, so it is what is drunk
• bibat is the verb inside the ut clause

That means Latin could rearrange the words for emphasis without changing the basic meaning. For example:

• Puero mater persuadet ut aquam puram bibat.
• Aquam puram mater puero persuadet ut bibat.

These are different in emphasis, but the grammar still makes the relationships clear.

Latin would normally use ne instead of ut in the subordinate clause.

So:

• Mater puero persuadet ne aquam puram bibat.

would mean:

• The mother persuades the boy not to drink pure water.

This is a useful contrast:

• ut + subjunctive = to do something
• ne + subjunctive = not to do something

You should learn the verb as:

• persuadeo, persuadere, persuasi, persuasum

That tells you:

• persuadeo = I persuade
• persuadere = to persuade
• persuasi = I persuaded
• persuasum = persuaded

In the sentence, persuadet is the third person singular present active indicative:

• he/she/it persuades

Since the subject is mater, here it means:

• the mother persuades