Learning Perfect Square

Introduction :

             A perfect square is a value which has a rational number as its square root. For example, 16, 27, 64, 1/4, 1/64 are all perfect squares. A trinomial that is in type of kx^2 + lx + m^2 and can be expressed in the form of square of a binomial let say, (px + q) ^2 is also a perfect square. In learning perfect square if an integer can be represented as a square of a different integer it is called as perfect square. It is also sometimes called as a square number.

 

Concept of learning perfect square:

 

            Square of number is multiplying the same number twice. A × A =A2, here square of A is written as A2 Here A is called the base and 2 is called the index or the power. Now observe the following examples:

            0^2 = 0 ×0 = 0

            1^2 = 1 ×1 = 1

            2^2 = 2 ×2 = 4

          These examples are square the same number. The square of 0,1,2,3,4 are 0,1,4,9,16 respectively. These square numbers are known as perfect squares.

In learning perfect square the next doubt some one acquire is will a negative integer be a perfect square. Solution is no because a perfect square number square root should be an integer. But a negative integer does not have some square root that is it will result in a difficult number but not an integer. This violates our fundamental rule. So all positive integers which can be expressed in the type n2 (where n=0, 1, 2, 3.......) is called as a perfect square.

 

Example problems for learning perfect square:

 

(1). Find the Perfect square of 30 on learning perfect square.

Solution:

              302 = 30 * 30

                    = 900

(2). Find the Perfect square of 111 on learning perfect square.

Solution:

          1112 = 111 * 111

                 = 12321

(3). Find the Perfect square of 12 on learning perfect square.

Solution:

         122 = 12 * 12

               = 144

(4). Find the Perfect square of 81 on learning perfect square.

Solution:

      812 = 81*81

            = 6561

(5). Find the Perfect square of 500 on learning perfect square.

Solution:

    5002 = 500 * 500

            = 250000