Az úszósapka és az úszószemüveg tiszta.

Both a and az mean the. Hungarian uses az before a word that begins with a vowel sound, and a before a consonant sound.

Here, both nouns begin with ú-, so you get:

• az úszósapka
• az úszószemüveg

If the noun started with a consonant, you would normally use a instead.

Because both nouns are definite and both are separate items in the coordination.

Hungarian normally says:

• az úszósapka és az úszószemüveg

rather than leaving the second article out. Repeating the article makes it clear that you mean the swim cap and the swimming goggles as two specific things.

In Hungarian, the present-tense forms of to be are usually omitted in the 3rd person when the sentence means something like X is clean or X is a teacher.

So:

• Az úszósapka tiszta. = The swim cap is clean.
• Az úszósapka és az úszószemüveg tiszta. = The swim cap and the swimming goggles are clean.

This is completely normal Hungarian.

But the verb does appear in other situations, for example:

• Az úszósapka tiszta volt. = The swim cap was clean.
• Az úszószemüveg az asztalon van. = The swimming goggles are on the table.

This is a very common learner question.

In Hungarian, when two singular nouns are joined by és, the predicate can often stay in the singular, especially in simple descriptive sentences like this one and especially with things rather than people.

So:

• Az úszósapka és az úszószemüveg tiszta.

is natural and correct.

You may also come across plural agreement in other contexts, but for a beginner, the safest thing is to learn that Hungarian does not always match English plural agreement in exactly the same way.

Yes. Hungarian uses compounds very often.

• úszó is related to úszni = to swim
• sapka = cap
• szemüveg = glasses / goggles

So:

• úszósapka = swim cap
• úszószemüveg = swimming goggles

Hungarian usually writes these as one word.

Because Hungarian often treats things like glasses or goggles as a singular noun referring to one pair.

So:

• az úszószemüveg = the swimming goggles / the pair of swimming goggles

If you wanted to talk about several pairs, then you would use a plural form.

This is similar to how languages sometimes group paired objects differently from English.

They are in the basic subject form, often called the nominative.

Hungarian marks many roles with endings, but the subject usually has no special ending. In this sentence, both nouns are simply the subject of the sentence, so they appear in their dictionary form:

• úszósapka
• úszószemüveg

The given order is the most neutral and straightforward one:

• Az úszósapka és az úszószemüveg tiszta.

This is the best version for a learner to use.

You can move words around in Hungarian, but word order often changes the emphasis. If you put tiszta earlier, it can sound more contrastive or marked, not just neutral.

So for ordinary descriptive statements, stick with the original order.

A few useful pronunciation points:

• sz sounds like English s
• Hungarian s sounds like English sh
• ú and ó are long vowels
• ü has no exact English equivalent; it is similar to German ü
• stress is normally on the first syllable of each word

Very rough pronunciation:

• az ≈ awz
• úszósapka ≈ OO-soh-shawp-kaw
• és ≈ aysh
• úszószemüveg ≈ OO-soh-seh-myoo-veg
• tiszta ≈ TIS-taw

That is only an approximation, but it is a useful starting point.