A "regular tetrahedron" is a four-sided solid where each side is an equilateral triangle. In other words, it's a triangular pyramid with six sides of equal length. Now, suppose that such a pyramid is sitting on a flat surface and that each of its sides measure 1000 meters.

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How tall is the pyramid? That is, what is the (exact) elevation of its top point?

Note: your answer must be exact! It will contain some square roots.