In 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".
12 = 1 x 1 = 1
22 = 2 x 2 = 4
32 = 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.
400 is a perfect-square, 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
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
22 = 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.