A Method for finding Square Roots

Mathematics Teaching in the Middle School, 2013

Mathematics Education Forum Chitwan

This paper specially concentrates on finding the square roots of perfect as well as imperfect square numbers by the Vedic sutra Vilokanam. Generally, extracting the square root of a number is considered a tedious job. There are two methods taught in our present-day classroom by conventional approach to find square roots, which are lengthy and time consuming. But, the Vedic Sutra Vilokanam helps us to find square root of such numbers with a little practice. The technique mentioned for extracting square root for imperfect square numbers does not belong solely to Vedic Mathematics written by Swami Bharati Krishna Tirthaji Maharaja. Mathematicians have been using it as a part of their general practice. However, the technique for calculating square roots and described in Vedic Mathematics is difficult. The methods discussed and organization of the content of the paper here are intended to show the Vedic Mathematics as an extremely refined and efficient mathematical system than convention...

Computing, 1979

Square Rooting Is as Difficult as Multiplication. It is shown that multiplication of numbers and square rooting have the same complexity, i.e. from a program for multiplication one can construct a program for square rooting with the same asymptotic time complexity (1 step ~ 1 bit-operation) and vice versa. It follows from the Schfnhage-Strassen algorithm that square rooting can be performed in 0 (n log n log log n) bit-operations. Die Komplexitiit des Wurzelziehens. Es wird gezeigt, dab Multiplikation von Zahlen und Bestimmen der Quadratwurzel yon gleicher Komplexit/it sind, d.h. aus einem Programm zur Multiplikation kann man eines zum Wurzelziehen konstruieren, das gr6Benordnungsm/~Big die gleiche Zeitkomplexit~it hat (1 Schritt ~ 1 Bit-Operation) und umgekehrt. Mit dem Schrnhage-Strassen-Algorithmus erhMt man so einen 0 (n log n log log n)-Algorithmus zum Berechnen der Quadratwurzel. 0 0 k A log Denotations the set of natural numbers {1, 2 .... } ,. f (n) f=0 (g) for two functions f, g : N ~ N means that nm sup-< oo .~ g (n) f-0 (g) means that f = 0 (g) and g = 0 (f) for x > 0, Lxa = max {y e N w {0} ] y_< x} logarithm to the base 2

https://www.ijrrjournal.com/IJRR_Vol.6_Issue.3_March2019/Abstract_IJRR0034.html, 2019

In this paper, we discuss about a new approach of finding square firstly in Arithmetic form and thereafter write the method (formula) in Algebraic form. The new method is mainly based on two steps, namely steps 1 and steps 2. After adding this step we find the result. This method may be named as two steps method of finding square or squaring of any digit numbers.

arXiv (Cornell University), 2023

This work presents and extends a known spigot-algorithm for computing square-roots, digit-by-digit, that is suitable for calculation by hand or an abacus, using only addition and subtraction. We offer an elementary proof of correctness for the original algorithm, then present a corresponding spigot-algorithm for computing cube-roots. Finally, we generalize the algorithm, so as to find r-th roots, and show how to optimize the algorithm for any r. The resulting algorithms require only integer addition and subtraction.

2022

This paper gives a heuristic equipment execution to registering square root activity for positive genuine numbers through Taylor arrangement and Newton's technique. Comparable methodology can be utilized for planning other root activities, for example, 3D shape roots, fifth roots, etc. Two unique structures are examined, one, combinational, straight forward, got from Taylor arrangement development and one consecutive, got from Newton's enhancement condition. The results are better, lower region, and lower power utilization for the subsequent engineering contrasted with the first.

Applied Mathematics and Computation, 2007

A one parameter family of iterative methods for solving nonlinear equations is constructed. All the methods of the proposed family are cubically convergent for a simple root, except one particular method which attains the fourth order without the increase of computational cost. These methods belong to the class of two-step methods and require three function evaluations per iteration. The square-root structure of the family provides finding a complex zero of real functions in some cases. A comparison analysis shows that the presented family generates the methods which are comparable or even superior than the existing two-step iterative methods of the third order.

The aim of this paper is to present a new method called "Restriction Method for Approximating Square Roots", that helps students to find an approximate value for any square root of positive Rational Number with an easy and simple way. Also, we prove this method and we give some examples that enhance our method.

Advances in Pure Mathematics

This paper presents a Method for the squaring of a circle (i.e., constructing a square having an area equal to that of a given circle). The construction, when applied to a given circle having an area of 12.7 cm 2 , it produced a square having an area of 12.7 cm 2 , using only an unmarked ruler and a compass. This result was a clear demonstration that not only is the construction valid for the squaring of a circle but also for achieving absolute results (independent of the number pi (π) and in a finite number of steps) when carried out with precision.

ETF Journal of Electrical …, 2004

Three algorithm implementations for square root computation are considered in this paper. Newton-Raphson's, iterative, and binary search algorithm implementations are completely designed, verified and compared. The algorithms, entire system-on-chip realisations and their functioning are described.