Жёсткость воды осталась высокой.

Because жёсткость воды means the hardness of water.

In Russian, a noun like жёсткость often takes another noun in the genitive to show what the quality belongs to:

• жёсткость воды = the hardness of water
• цвет неба = the color of the sky
• температура воздуха = the temperature of the air

So вода becomes воды because it is the thing whose hardness is being discussed.

Because after the verb остаться (to remain), Russian usually puts the predicate adjective in the instrumental case.

So:

• высокая = nominative feminine singular
• высокой = instrumental feminine singular

In this sentence:

• Жёсткость is the subject
• осталась is the verb
• высокой describes the state that the subject remained in

This is a very common pattern after verbs such as:

• быть = to be
• стать = to become
• оставаться / остаться = to remain

Examples:

• Она была уставшей. = She was tired.
• Он стал врачом. = He became a doctor.
• Погода осталась тёплой. = The weather remained warm.

Because the subject is жёсткость, and жёсткость is a feminine singular noun.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine: остался
• feminine: осталась
• neuter: осталось
• plural: остались

So:

• Жёсткость → feminine singular
• therefore осталась

Осталась is the past tense of остаться, which means to remain, to stay, or to be left depending on context.

Here it means remained:

• Жёсткость воды осталась высокой.
• The water hardness remained high.

It suggests that the hardness was high before, and after some point or event, it was still high.

So there is often a nuance of no change or continuation of a state.

Because осталась and была are not exactly the same.

• Жёсткость воды была высокой. = The water hardness was high.
• Жёсткость воды осталась высокой. = The water hardness remained high.

Была simply states a past fact.

Осталась adds the idea that the hardness continued to be high, often despite expectations that it might change.

For example, if water was treated or filtered, but the hardness did not go down, Russian would naturally use осталась.

Осталась is the perfective past form of остаться. It presents the situation as a completed fact: at the relevant point, the hardness ended up remaining high.

Оставалась is the imperfective past form. It would emphasize duration, process, or repeated/ongoing background description.

Compare:

• Жёсткость воды осталась высокой.
  The water hardness remained high.
  (a complete fact/result)

• Жёсткость воды долгое время оставалась высокой.
  The water hardness remained high for a long time.
  (emphasis on duration)

So in your sentence, perfective осталась fits a simple factual result very well.

The adjective agrees with жёсткость in gender and number, but its case is determined by the construction after осталась.

Here:

• жёсткость = feminine singular
• so the adjective must also be feminine singular
• because of осталась, it appears in the instrumental

That gives:

• dictionary form: высокий
• feminine nominative: высокая
• feminine instrumental: высокой

So высокой means something like high in the form required by the sentence structure.

Yes. Russian word order is fairly flexible, although the original order is the most neutral:

• Жёсткость воды осталась высокой.

Other orders are possible, but they change emphasis:

• Высокой осталась жёсткость воды.
  Emphasizes high
• Осталась высокой жёсткость воды.
  Slightly more literary or stylistic

A learner should usually treat Жёсткость воды осталась высокой as the standard neutral version.

Жёсткость is pronounced roughly like ZHYOST-kastʹ.

A few useful points:

• ё is always stressed
• жё sounds roughly like zhyo
• the final ь is a soft sign; it does not make its own sound, but it affects pronunciation

The word comes from жёсткий (hard, rigid), and жёсткость means hardness or rigidity, depending on context.

In everyday printed Russian, ё is sometimes written as е, so you may also see Жесткость, but it is still understood as Жёсткость here.

Yes, very common.

Russian often expresses this kind of idea with a noun + genitive structure:

• жёсткость воды = water hardness
• давление газа = gas pressure
• температура тела = body temperature

So even though English often uses one noun before another (water hardness), Russian usually prefers hardness of water structure: жёсткость воды.

Yes, that is also possible, but it is slightly different in focus.

• Жёсткость воды осталась высокой.
  Focuses on the measurable property: hardness remained high.
• Вода осталась жёсткой.
  Focuses on the water itself: the water remained hard.

In scientific, technical, or formal contexts, жёсткость воды is often more precise.