In mathematics, a square number or perfect square is an integer that is the square of an integer;[1] in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3. The usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n2, usually pronounced as "n squared". The name square number comes from the name of the shape. The unit of area is defined as the area of a unit square (1 × 1). Hence, a square with side length n has area n2. If a square number is represented by n points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples being cube numbers and triangular numbers).

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As explained in the introduction part, natural numbers are the numbers which are positive integers and includes numbers from 1 till infinity(∞). These numbers are countable and are generally used for calculation purpose. The set of natural numbers is represented by the letter “N”.

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When a number or integer (not a fraction) is multiplied by itself, the resultant is called a ‘Square Number’. For example, 3 multiplied by 3 is equal to 3-squared or 3 x 3 = 32. So, basically, the exponential form of multiplication of a number or integer by itself is called a square number. Also, if we again multiply the number by itself, then we get a cube of the integer., a x a x a = a3. Square numbers are always positive. If negative sign is multiplied by itself, it results in positive sign (+). For example, (-4)2 = 16. So, we can say here 16 is a positive square number, whose square root is an integer again, i.e.√16 = 4. In geometry, a square shape has all its sides equal. Therefore, the area of the square is equal to the square of its side. Area of a square = Side x Side = Side2 Therefore, we can say. Square number = a x a = a2

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In Mathematics, the circumference of any shape defines the path or the boundary that surrounds the shape. In other words, the circumference is also called the perimeter, which helps to identify the length of the outline of any shape. As we know, the perimeter and area of circle are the two important parameters of a circle. In this article, we will discuss the “Circumference of a circle” or “Perimeter of circle” with its definition, formula, methods to find the circle’s circumference with many solved examples.

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A branch of mathematics that talks about the length, volume, or area of different geometric shapes is called Mensuration. These shapes exist either in 2-dimensions or 3-dimensions. Let’s learn the difference between the two.

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Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

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The polynomial division involves the division of one polynomial by another. The division of polynomials can be between two monomials, a polynomial and a monomial or between two polynomials. Before learning how to divide polynomials, let’s have a brief introduction to the definition of polynomial and its related terms.

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The algebraic equations which are valid for all values of variables in them are called algebraic identities. They are also used for the factorization of polynomials. In this way, algebraic identities are used in the computation of algebraic expressions and solving different polynomials. You have already learned about a few of them in the junior grades. In this article, we will recall them and introduce you to some more standard algebraic identities, along with examples.

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To factorize an algebraic expression, the highest common factors of the terms of the given algebraic expression are determined and then we group the terms accordingly. In simple terms, the reverse process of expansion of an algebraic expression is its factorization.

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The term graph can refer to two completely different things. Students usually first learn of a graph as plot of a function, or a function graph. Here, we refer to a different definition of graph, in which a graph is another word for a network, i.e., a set of objects (called vertices or nodes) that are connected together

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The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is x = 5/2. Whereas if we speak about linear equation in two variables, it has two solutions.

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