Learn Farsi: بعد از اینکه خاک را آزمایش کردید، بازدهی آن تا چه اندازه بهبود یافت؟ - After you tested the soil, to what extent did its yield improve?

Yes, they are completely interchangeable here. تا چه اندازه literally means "up to what measure," while تا چه حد means "up to what limit." Both perfectly translate to "to what extent" when asking about the degree of the soil's improvement.

Why does this sentence use بعد از اینکه instead of just بعد از?

بعد از is a preposition used before simple nouns, like بعد از آزمایش (after the test). Because "you tested the soil" is a complete clause with a conjugated verb (آزمایش کردید), you must use اینکه to act as a bridge connecting the preposition to the full clause.

I know بهتر شدن means "to get better." Why use بهبود یافت for "improved" here?

بهبود یافتن (literally "to find improvement") is a more elevated compound verb often used for conditions, health, or scientific metrics like agricultural yield. In casual spoken Farsi, you could easily say بهتر شد (became better), but بهبود یافت is the standard choice for professional or written contexts like this one.

How does the phrase بازدهی آن work here, and what does آن refer to?

بازدهی means "efficiency," "productivity," or "yield." The pronoun آن (it/that) refers back to the soil (خاک). They are linked by the ezâfe vowel (pronounced ), literally meaning "the yield of it" or "its yield."