Properties of squares





Here we are going to see some of the properties of squares.

1. Observe the following:

1 2 = 1
2 2 = 2
3 2 = 9
4 2 = 16
5 2 = 25
6 2 = 36
7 2 = 49
8 2 = 64
9 2 = 81
10 2 = 100

It is observed that the squares of the first 10 natural numbers end in 0, 1, 4, 5, 6, 9…….It denotes that the numbers ending with 2,3,7,8 are not a perfect square. We can easily say that the numbers 22, 23,207,248 etc should not perfect squares. It is not necessary that the numbers which end with 0, 1,4,5,6 and 9.

Here is the second and third property of properties of squares.

2. Squares of even numbers are always even. For example 16 is the even number its square value is 256.It is also even number.

3. Squares of odd numbers are always odd.For example 15 is the odd number its square value is 225.It is also odd number.

4. If a, b, c are there numbers such that a2 = b2 + c 2 , then a, b, c are called Pythagorean Triplet.

5. Study the following patterns:

1 = 1
1 + 3 = 4 = 2 2
1 + 3 + 5 = 9 = 3 2
1 + 3 + 5 + 7 = 16 = 4 2
……………………………………..
……………………………………..
1 + 3 + 5 + ………… + 20 term = 20 2

Hence we can decide that the sum of first n odd number is n 2

We can also express that the square of any natural numbers as the sum of odd numbers.Here are some examples.

(i) 1 + 3 + 5 + 7 + 9 = 25
(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 = 81



Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”






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