Archive for February 11th, 2008

Root extraction, part II: cube roots

February 11, 2008

dandelion-root.jpgAs you might guess, this post builds on “Root extraction, part I“, which gave a way to visualize the traditional square root algorithm geometrically, an approach that has the advantage that each step appears natural and easily motivated.

Our goal herein is to do much the same for cube roots. The point is to find a geometric construction, ideally one well-suited to physical manipulatives, in which the steps in building the successive digits of the cube root of a number are transparent.  As with the post on square roots, I make no claims to originality in what follows.

Example:  Find \sqrt[3]{22665187}(more…)