Square of numbers ending with
5
It’s
simple logic, any multiplication of 5 will end with 25, so at end of the result
it will be 25, in the result starting, it will be the multiplication of n *
(n+1)
For
Eg: 35 * 35
Where
n = 3,
3 * (3+1) = 3*4 = 12.
Append
25 to the result the answer is 1225
5
15
25

5
15
25

=
=
=

0 * (0+1) 25
1 * (1+1) 25
2 * (2+1) 25

25
225
625

Square of numbers ending with 1, 4, 6 and 9.
There is a small
logic for this numbers ending.
For 1 and 6
26^{2} = 25^{2
}+ (25+26) = 625 + 51 = 676
71^{2} = 70^{2}
+ (70+71) = 4900 + 141 = 5041
For 4 and 9
24^{2} = 25^{2}
– (25+24) = 625 – 49 = 576
69^{2} = 70^{2}
 (70+69) = 4900  139 = 4761
Square root for four digit number.
First right out the
squares from1 to 9.
1
1
2
4
3
9
4
16
5
25
6
36
7
49
8
64
9
81

Number ends with
1 1
and 9
4 2
and 8
9 3
and 7
6 4 and 6
5 5

For Ex: find the square root for 1156
Now, Split the number 1156 as 11 and 56
Check where the first split
lies between the nearest squares.
9
≤ 11 ≤ 16
3^{2
}≤ 11 ≤ 4^{2}
The lowest nearest one has to
be taken here. Means, we are going to take 3.
So, the result of the first number will be 3
So, the result of the first number will be 3
Multiple with n+1 number, for
ex, the lowest nearest one is 3, then n=3.
So, multiple n with n+1 as
below
3
* 4 = 12
Check whether 12 is less than 11 or not.
Since the unit number of 1156 is 6, as per the table the number can be 4 or 6.
If it is less take 4 else 6.
Since 12 is greater than 11,
we are going to take 6.
So, the square root of 1156 is 36.
One
More Ex:
Let
check for 2401
Split number 24 and 01
16 ≤ 24 ≤ 25
4^{2 }≤ 24 ≤ 5^{2}
4*5 = 20
Unit
digit is 1, so the result of end
number can be 1 and 9
24 is the first split one,
Check
20 with 24 is greater than or less than the first split number,
20 < 24
So
take 9.
Result = 49
Let
check for 1681
Split number 16 and 81
16 ≤ 16 ≤ 25
4^{2 }≤ 16 ≤ 5^{2}
4*5 = 20
Unit
digit is 1, so the result of end
number can be 1 and 9
16 is the first split one,
Check
whether 16 with 20, 20 > 16, and so take 1.
Result = 41