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 ^{ 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 } = 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 ^{ 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
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