## Amazing Properties of Squares & Their CalculationsAmazing Properties of Squares & Their Calculations is a humble endeavor of the author to write a book on speed arithmetic. The book contains some of the very exciting facts about squares of natural numbers. This book illustrates some special types of numbers and calculation of their squares. The author also attempts to explain and illustrate the general concepts on square calculation. This book is the Bible on calculation of squares and properties of squares. Each chapter is independent of each other. Hence, no particular reading order is recommended for this book. Some of the chapters are very useful in preparing for competitive exams. Book assumes no other prior mathematical background to grasp the concepts explained in this book. The only pre-requisite to read this book is to have prior knowledge about tables of 1 to 10 numbers and squares of 1 to 25 numbers. Following are the salient features of this book...- This book contains originality. It means in most chapters things are discussed, which we will not find in any other book on speed arithmetic. Even if particular concept is found in some book or website, author has represented it in a little different way.- It is useful for competitive exam- Author has given enough examples on each type of square calculation of a number (minimum 3 examples) so that reader will not have any doubt.- Almost all the chapters are having different style from traditional learning maths taught in school or college or in books.- Each chapter has been discussed separately without any prior knowledge of previous chapters so that reader can read any chapter independently and can move in any order in reading this book.- The approach used in this book is on calculation of last two digits of a square which is different from other approaches.This book will develop high interest levels in people who have do not have passion for mathematics can develop liking for math not only in calculation of squares but also in other areas like multiplication and division.- Till now methods like casting out 9's and casting out 11's were used in checking calculation , but in this book in chapter 17 and 18 these two methods are used to calculate square of two and three digit numbers respectively which is a very new thing.- Examples are explained step by step and are plenty in number and any student above seventh standard can understand it. Also topics range from elementary to medium level.- All the methods to calculate square of a number that are present in other books are discussed here in addition to some new methods. Following are the methods discussed in this book to calculate square of a general number.Chapter 6, Algebraic Identity (a+b)2 square calculationChapter 7, Square calculation using a2 = b2 + (a+b)*(a-b) formulaChapter 8, Vedic Mathematic Method Chapter 9 and 10, Two digit numbers method generalization for 3 and 4 digit numbers.Chapter 13, Square of a no. near to power/multiple/sub-multiple of power of 10 Chapter 14, Vedic Mathmetic's 'Urdhva Tiryak' method Chapter 15, Ratio Method uses ratio of two successive digitsChapter 16, Vinculum calculation method, often used to calculate big digits are bigChapter 17, Square of two digit number using casting out 9's methodChapter 18, Square of three digit number using casting out 9's and casting out 11's method- Theory behind every concept is explained which will help keen maths students proud. Superficial readers can use last result given in theory.- Various square calculation methods for number like 97 using (a+b)2 formula, Vedic maths method (100-x)2 = 100-2*x | x2, method to calculate square of a number near to power of 10, Vedic 'Urdhva Tiryak' method, Ratio method, Vinculum method, and Casting out 9's. You would learn different methods to calculate any square.- Chapters 11 and 12 are fun to read as specific digit or specific number repeated any no. of times can be squared using arithmetic progression method |

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answer Append digit calculating square digit casting out 9’s Category chapter common difference difference as sum digit 9 repeated digit base number digit no.1 digit no.2 digit square digit sum digits of R2 doubling fifth example followed by digit followed by unit formed by last formed by rightmost four digit number immediate left group integer keep one digit keeping digit know squares last two digits left of group leftmost digit Let us calculate means that digit number and digit number formed number from right number obtained number to multiply obtained by numbers original number Penultimate digit perfect square positive integer positive squares relatively easy number repeated n-1 rest digits retain only last right to leftwards rightmost digit rightmost two digits squares of numbers step is a2 sum of digits Suppose we want term and add term from right third term three digit number unit digit Vedic Mathematics book vinculum want to calculate