Finding Roots of Numbers

Abstract

The scope of Chapter 2 is square roots of numbers: how to find them and how to compute with them. (Cube roots are discussed in Chapter 5.) Not only are the readers instructed on how to find square roots of up to six digit numbers, each clearly exemplified, but they are returned to the world of Pisan units of measurement and shown how to find the roots of square units of rod, feet, and inches, not to overlook a digression into the astronomical world of square degrees, minutes, seconds, and thirds (!). Fibonacci offered two ways of proving that a root is what it claims to be, the obvious method of multiplying a number by itself and one that suggest modular arithmetic [11]. Noteworthy is the fact that he made no reference to any of the geometric theorems discussed at length in Chapter 1, even if the reader can see where some are applied. In grappling with large numbers such as 9876543 he advised the reader to find first the root of the last five digits (98765). Next and after joining any remainder to the remaining digits (43), find its root. And then simply put the two roots together as one root. Finally, and after a practical definition of radix, the readers are instructed on how to add, subtract, multiply, and divide radicals.