Learn Turkish: Otel kuruluştan beri çok kalabalık. - The hotel has been very crowded since its foundation.

The postposition beri (since) requires the noun before it to take the ablative case (the "from" suffix). So, you must attach -tan to kuruluş to make it work with beri.

Why does the ablative suffix take the form -tan here instead of the usual -dan?

The word kuruluş ends with the voiceless consonant ş. Because of Turkish consonant harmony (often remembered by the "Fıstıkçı Şahap" rule), the d at the start of the suffix hardens into a t, giving us -tan.

The English translation says "has been very crowded", but there is no past tense verb in the Turkish sentence. Why?

In Turkish, if a state started in the past and is still true right now, you just use a present tense sentence. The word beri already tells the listener that this has been going on "since" a certain time, so you don't need a special "has been" verb tense like you do in English.

What is the root of the word kuruluş?

It comes from the verb kurmak (to establish or set up). By adding suffixes, it becomes the noun kuruluş, which means "establishment" or "foundation".