Press your lips together to stop the air, then release. No vocal cord vibration.

Americans pronounce prosperity as prah-SPAIR-uh-tee (/prɑˈspɛrəɾi/). In "prosperity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. This is called the Flap T, a small move that separates 'classroom' from 'native'. It comes out as prah·SPAIR·uh·tee. Stress falls on the second syllable — keep everything else short and quick. You'll hear it in sentences like "I hope this coming year brings you joy, health, and prosperity".
Record yourself saying "prosperity" and play it back. The mic stays on your device — nothing's uploaded.
4 syllables, 9 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Press your lips together to stop the air, then release. No vocal cord vibration.

Curl or bunch your tongue without letting the tip touch the roof of your mouth. Brace the sides of your tongue against your upper back teeth, and round your lips slightly.
Relax your lips and drop your jaw significantly. The tongue tip lightly touches behind the bottom front teeth and the back part of the tongue presses down a little to create more dark space in the back of the mouth.

Place your tongue tip near the roof of your mouth behind your top teeth. Push air through the narrow gap. No voicing.

Press your lips together to stop the air, then release. No vocal cord vibration.

Start with the 'eh' vowel mouth position. Pull the tongue back and up while flaring the lips for the 'r'.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "prosperity", the "t" between vowels sounds like a quick "d" — the tongue briefly taps the ridge behind the upper teeth. /t/ or /d/ becomes a quick tap [ɾ] — sounds like a soft D. The tongue briefly taps the ridge behind the upper teeth.
Stress falls on the second syllable, not the others. Stretch SPAIR — keep everything else short and quick.
Don't pronounce the second syllable too fully. The unstressed syllable reduces to a schwa — the lazy "uh" sound — in casual speech.
Americans use a relaxed retroflex R — the tongue curls back rather than rolling. The R is one continuous sound with the vowel before it, not two separate sounds.