Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Americans pronounce courtroom as KORT-room (/ˈkɔrtˌrum/). Stress falls on the first syllable — keep everything else short and quick. You'll hear it in sentences like "The judge entered the courtroom and everyone stood up" or "The bailiff maintained order in the courtroom throughout the proceedings" — more examples below.
Record yourself saying "courtroom" and play it back. The mic stays on your device — nothing's uploaded.
2 syllables, 6 sounds. Tap a syllable to jump to its row, then explore each sound's mouth shape and how it's made.
Raise the back of your tongue to touch the soft palate (velum). Stop the air, then release.

Start with the 'aw' jaw drop and rounded lips. Pull the tongue back and up while keeping the lips rounded for the R.
Touch the tip or front edge of your tongue to the roof of your mouth just behind your teeth. Keep your jaw relaxed. Stop the air, then release with a puff.

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.
Round your lips into a tight circle. Let your tongue rest in the middle of your mouth, slightly raised.
Press your lips together. Air flows through your nose. Vocal cords vibrate.

Click any sentence to see the full breakdown — every link, every reduction, every flap-T.
The textbook way isn't wrong — it's just not how anyone actually says it.
In "courtroom", the "t" is not released — the articulators get into position but hold without the burst of air. Air stops but there's no release burst — the articulators hold position.
Stress falls on the first syllable, not the others. Stretch KORT — keep everything else short and quick.
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.