Evaluating cube roots of small perfect cubes

Students will learn how to evaluate cube roots of small perfect cubes: 1, 8, 27, etc. Problems should include both positive and negative numbers, integers, decimals, and fractions. Students will also see that determining the side lengths of a geometric cube, given its volume, is the same as finding the cube root of its volume. Here's an excellent demonstration of this connection.

TODO: This may be a valid and interesting method for finding the cube root of large numbers, but it isn't explained well at all. Maybe I can deduce from the video what's going on and clean it up.