PROPERTIES OF PERFECT SQUARE

When a number is multiplied by itself, we say that the number is squared.

It is denoted by a number raised to the power 2.

For example,

3 x 3 = 32 = 9

5 x 5 = 52 = 25

In the example above, 52 is read as 5 to the power of 2 or 5 raised to the power 2 or 5 squared. 25 is the square of 5.

Similarly, 49 and 81 are the squares of 7 and 9 respectively.

The numbers 1, 4, 9, 16, 25, g are called perfect squares or square numbers as 1 = 12, 4 = 22, 9 = 32, 16 = 42  and so on.

A number is called a perfect square, if it is expressed as the square of a number.

We observe the following properties through the patterns of perfect squares.

Property 1 :

In perfect squares, the digits at the one’s place are always 0, 1, 4, 5, 6 or 9. The numbers having 2, 3, 7 or 8 at its one' place are not perfect square numbers.

Property 2 :

If a number has 1 or 9 in the one's place then its square ends in 1. Property 3 :

If a number has 2 or 8 in the one's place then its square ends in 4. Property 4 :

If a number has 3 or 7 in the one's place then its square ends in 9. Property 5 :

If a number has 4 or 6 in the one's place then its square ends in 6. Property 6 :

If a number has 5 in the one's place then its square ends in 5. Property 7 :

Consider the following square numbers : From the perfect squares given above, we infer that Property 8 :

A perfect square number followed by even number of zeros will be a perfect square and a perfect square number followed by odd number of zeros will not be a perfect square.

Consider the following square numbers : Therefore, 100 is a perfect square and 81000 is not a perfect square.

Property 9 :

Square of even numbers is always even. Property 10 :

Square of odd numbers is always odd. From property 11 and property 12, we infer that Some Interesting Patterns of Square Numbers

Addition of consecutive odd numbers : The above figure illustrates the result that the sum of the first n natural odd numbers is n2.

And, square of a rational number a/b is given by Kaprekar Numbers  Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

Kindly mail your feedback to v4formath@gmail.com

Recent Articles 1. Multiplicative Inverse Worksheet

Jan 19, 22 09:34 AM

Multiplicative Inverse Worksheet

2. Multiplicative Inverse

Jan 19, 22 09:25 AM

Multiplicative Inverse - Concept - Examples