Properties of Square Root

Let’s look at the square of numbers from 1 to 50

Let’s see some pattern in it, and find properties of square root

If a number ends with 1,

its square root will end with 1 or 9

Example:

As 1 ²  = 1

  & 9 ²  = 81

∴ √81 = 9

   √1 = 1

If a number ends with 6,

its square root will end with 4 or 6

Example :

As 4 ²  = 16

  & 6 ²  = 36

∴ √16 =  4

   √36 =  6

If a number ends with 5,

its square root will always end with 5

Example :

As 5 ²  = 25

  & 15 ²  = 225

∴ √25 =  5

    √225 = 1 5

If number has even number of zeroes at the end,

its square root will have half of it

Example :

         10 ²  = 100

200 ² =40000

So, 

If a number ends with 2, 3, 7, 8,

it is not a perfect square

Example :

2422, 373, 918, 27 are not perfect square.

So, their square root will be in decimals

If a number ends with odd number of zeroes,

it is not a perfect square

Example :

24000, 10, 2500000 do not have a square root

So, their square root will be in decimals

Square root of even number is even,

Square root of odd number is odd

Example :

Odd

  √1=1

  √9= 3

 √81=9

Even

    √4=2

  √16= 4

√100= 10

To summarize

• Unit digit of square roots have this property

• Square root of even number is even, odd number is odd
• A number is not a perfect square, if it ends with 2, 3, 7, 8 or if it has odd number of zeroes

Square root of Negative number is not possible

√(-9)  is not possible