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 = 2

Such numbes are known as

In general , if a natural number p can be expressed as q

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 4

6 = 2 x 3 6

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.

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

Since 4 can be expressed as 2 x 2 = 2

^{2}, 16 can be expressed as 4 x 4 = 4^{2}, 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 q

^{2}, 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 4

^{2}= 16 = 2 x 2 x 2 x 2 = 2^{2}x 2^{2}6 = 2 x 3 6

^{2}= 36 = 2 x 2 x 3 x 3 = 2^{2}x 3^{2}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.

Technically, in the prime factorization of a perfect square, every prime number occurs a

ReplyDeletemultipleof two times.144 = 2x2 x 2x2 x 3x3

But you're mostly right :D