You're asking about the distance between the Earth's inner core and the crust, but the question needs a slight correction. Here's why:

* Inner Core and Outer Core: The Earth's inner core is solid, and it's surrounded by the liquid outer core.

* Crust: The crust is the outermost layer of the Earth, above the mantle.

Therefore, we're looking at the distance between the inner core boundary (where the inner core meets the outer core) and the base of the crust (where the crust meets the mantle).

Here's the approximate distance:

* Inner core boundary to base of crust: ~2,890 km

This distance is based on current scientific estimates of Earth's structure. Keep in mind that these measurements are approximate and could vary slightly based on different studies.