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

Number Square root
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
100 10
121 11
144 12
169 13
196 14
225 15
256 16
289 17
324 18
361 19
400 20
441 21
484 22
529 23
576 24
625 25
900 30
1225 35
1600 40
2025 45
2500 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 = 1

  & 9 = 81

 

∴ √81 = 9

   √1 = 1

 

If a number ends with 6,

its square root will end with 4 or 6

Example :

As 4 = 16

  & 6 = 36

 

∴ √16 =  4

   √36 =  6

 

If a number ends with 5,

its square root will always end with 5

Example :

As 5 = 25

  & 15 = 275

∴ √25 =  5

    √275 = 1 5

 

If number as even number of zeroes at the end,

its square root will have half of it

Example :

         10 = 100

200 2 =40000

So, 

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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

One’s digit of Number

One’s digit of Square Root

1

1 or 9

6

4 or 6

5

5

Even number of zeroes

Half of it

  • 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

 

   

  1. Chapter 6 Class 8 Squares and Square Roots
  2. Concept wise
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.