On Programming the Integral RTH Root of a Number on Friden Standard and Square Root Desk Calculators
although its application for taking advantage of the square-root feature on certain Friden Calculators is believed to be new. The m at he m atics of the derivations are given in the third section of the paper since this information is probably of least interest to those who will operate with the form ulas. The second section contains three examples. The cube root example is symbolically pro grammed for the c al c ul ator in s e c tion 4. Ta ble I presents a set of f ormulas which are effi cient for finding the rth root of a real number. That is, for finding the square root, cube root, etc., of some number, N. The symbol xin the formulas stands for a guessed or trial value of the root and cone ei vably may be grossly in error. However, if it is considerably in error, the form ulas will ultimately provide an accurate estimate of the root although it will take a longer time than if an estimate only slightly in error were used. The method to us e with the formulas involves essentially selectinga trial value, substituting this (as x) in the appropriate formula and there by obtaining a new trial value. This new value is again substituted in the formula (as x). This iter ation process is repeated until the desired deci mal accuracy is obtained. The formulas in Table I have been arranged so that the arithmetic ultimately involves the accu mulation of two quotients. Therefore, the proper machine set-up requires the NON ENT key to be down. Also it is advisable that the ADD key is in the down position. In some of the f o r m ul as the divisors of x appear as improper fractions (e. g., -5-). In actual computations, these numbers can be changed to decimals appropriate to the accu racy required or the problem can be treated as a simple quotient (e.g., 3x/4). The Square Root Friden enables all roots of the form r = 2*, where i = 1, 2,3,..., of a number to be taken directly without the use of any special formulas. For instance, to obtain the fourth root of 2. 0000 we merely find the -?2 = 1.41421 and then find VI. 41421 = 1.1892 which is an accurate esti i