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Number System is a system of representing numbers using symbols and digits in a certain manner. One can think of it as a Grammar book in mathematics. As soon as one hear this word “Number” 1,2,3,…. get pop in one’s head immediately. Number System defines their value, operations to perform, and other properties. Each number is unique. It has many variations. Thus, it can be considered as a natural number, whole number, even number, odd number, prime number, composite number, etc.
Algebra is the branch of Mathematics that emphasizes the use of various symbols and mathematical operations that can be performed on them. In Algebra, symbols such as alphabets are used like a, b, c or x, and many others whose value is not predefined. Their value is not fixed, hence called variables. One can declare any amount of variables and define the specific value to them. These symbols or variables can be manipulated with help of arithmetic operations like addition, subtraction, multiplication, and division. Let us deal with one application of Algebra which is Algebraic Expression. An algebraic expression is composed of coefficients, Terms, Variables, and Constant, etc. and people have to determine the value of an unknown variable with mathematical operations. Natural NumbersNatural numbers are the counting numbers that begin from 1 till infinity, They are used for counting purposes. e.g. 1,2,3,4,…. , are natural numbers. Basically, Natural numbers are an integral part of the real number system.
A set of Natural numbers is denoted by N such that N = {1, 2, 3, 4, 5, 6, 7, 8,….}. Use algebra to prove that the square of any natural number is either a multiple of 3 or one more than a multiple of 3.Solution:
Similar ProblemsQuestion 1: Prove that the sum of two consecutive square numbers is odd? Solution:
Question 2: Prove that if m is not the square of a natural number, then √m is irrational. Solution:
Question 3: Prove that if n is a natural number, then √n is irrational or a natural number. Solution:
Question 4: Prove that product of two perfect square numbers is also a perfect square. Solution:
Learn more about Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you Algebra: Structure And Method, Book 1 Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole Publisher:McDougal Littell Glencoe Algebra 1, Student Edition, 9780079039897... Algebra & Trigonometry with Analytic Geometry Algebra for College Students Author:Jerome E. Kaufmann, Karen L. Schwitters Publisher:Cengage Learning Algebra: Structure And Method, Book 1 ISBN:9780395977224 Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole Publisher:McDougal Littell Glencoe Algebra 1, Student Edition, 9780079039897... ISBN:9780079039897 Author:Carter Publisher:McGraw Hill Algebra & Trigonometry with Analytic Geometry ISBN:9781133382119 Author:Swokowski Publisher:Cengage Algebra for College Students ISBN:9781285195780 Author:Jerome E. Kaufmann, Karen L. Schwitters Publisher:Cengage Learning |