Thursday, June 28, 2012

Square Numbers - I

We know that the area of a square = side x side. Let us study the following table :


What is special about the numbers 4 , 9 , 16 , 36 and other such number ?

Since 4 can be expressed as 2 x 2 = 22 , 16 can be expressed as 4 x 4 = 42 , all such numbers can be expressed as the product of the numbers with itself.
Such numbes are known as square numbers.

In general , if a natural number p can be expressed as q2 , where q is also a natural number , then p is a square number. Square numbers are also called perfect squares.

How can we check whether a number is perfect square of not , let see the following square numbers and their prime factors :

 4 = 2 x 2       42 = 16 = 2 x 2 x 2 x 2 = 22 x 22
 6 = 2 x 3      62 = 36 = 2 x 2 x 3 x 3 = 22x 32 

Thus we can see that in the prime factorization of a perfect square , every prime number occurs two time. We can define the following algorithm to check a number is perfect square or not. 

Step 1 – Find the prime factors of the given number. 
Step 2 – Group the factors into pairs of like factors. 
Step 3 – If all the factors can be paired , then the given number is a perfect square , otherwise it is not.

In my next post I will discuss some properties and interesting facts about the square number. Happy Reading.

1 comment:

  1. Technically, in the prime factorization of a perfect square, every prime number occurs a multiple of two times.

    144 = 2x2 x 2x2 x 3x3

    But you're mostly right :D

    ReplyDelete