A digital designer's book devoted entirely to roots, technically call radicals. First of its kind. Relevant theory is also provided with associated diagrams and operational parameters. A collection of algorithms taken from white papers and text books include square roots, cube roots, and nth root. The first two, square and cube roots, each have a simple and high performance implementation. The nth root can support square, cube, 4th, and 5th root extraction on the fly. All designs are fully coded utilizing state machines in VHDL. Implementations are fixed-point and have scalable operands based on constants.