## What are Square and Square Roots ?

## How to identify if number is perfect square

From the above chart we see all perfect square numbers units place is 0,1,4,5,6,9 and so we can say that if the square of any number ends with one of the above i.e 0,1,4,5,6,9 then that number is perfect square.

For example: 12**3** is not perfect square because its units place is 3

324**5** is perfect square because its units
place is 5

Also, note one more thing that if the number has 1 or 9 in units place then its square ends with 1 in units place.

And one more thing that if the number has 4 or 6 in units place then its square ends with 6 in units place.

Lets see one more thing, In between these perfect squares there are other not perfect squares which are odd numbers.

If we add odd numbers we get perfect squares

1+3 =4 =square of 2

1+3+5 = 9 = square of 3

1+3+5+7 =16= square of 4

1+3+5+7+9 =25= square of 5

1+3+5+7+9+11=36 =square of 6

1+3+5+7+9+11+13 = 49 = Square of 7

So we can say that *if a natural number cannot be* *expressed as a sum of successive odd natural numbers* *starting with 1, then it is not a perfect square*.

For small numbers we can easily find the square root on number, how to find out for big numbers ?

How to find square of 23

23 can be written as 20+3, means

i.e (20+3) X (20+3) = (20+3) X 20 + (20+3) X 3

((20×20) + (20×3)) + ((20×3) + (3×3))

400 +60 + 60 +9 = 529

### How to find square roots

Square root of numbers can be find out by prime factorisation, which means factorising the numbers with prime numbers

Lets find out the square root of 16