


SquareIn this topic square we are going to see the meaning of squares and example problems.When a number is multiplied by itself twice, the product so obtained is called the square of that number. it is denoted as,"number which is having power 2". Examples: 1^{2} = 1 x 1 = 1 2^{2} = 2 x 2 = 4 3^{2} = 3 x 3 = 9 In order to find whether a given number is perfect squre or not, write the number as a product of its prime factors.
1. If a number ends in zero, we can immediately decide whether it is a perfectsqure or not. It may be observed that the number of zeros in the end of a perfect square is never odd. Examples: 400 is a perfectsquare, the number of zeros is two even 4000 is not a perfect square, the number of zeros is three 2. The difference between the squares of two consecutive number is equal to the sum of the numbers Examples: 25 ^{ 2}  24^{ 2} = 25 +24 15^{ 2}  14^{ 2} = 15 +14 525 ^{ 2}  524^{ 2} = 525 + 524 3. If the factors can be grouped in pairs in such a way that both the factors in each pair are equal, we call the given number as a perfect square. Let us observe the following patterns 2^{2} = 4 = 4 x 1
The above patterns suggest that (i) The square of a number (other than 1) is either a multiple of 3 or exceeds a multiple of 3 by 1. Let us see the example problems below
We observe that the prime factors of 196 can be grouped into pairs as shown and no factors in left over. 196 is a perfect square. It is square of 2 x 7 = 14.


