Just remember squares upto 25.
Check the difference from 50 and add or subtract it from 25 and by the side of this number you have to write the square of that difference in 2 digits only (in case of 1, write 01).
For example: if you have to find square of 43
Difference from 50, i.e. 43 is 7 less than 50. So subtract 7 from 25, and you will get 18 and square of (-7) is 49.
So 43^2 = 1849
If you have to find square of 53,
Difference from 50 is 3, so adding 3 to 25, you will get 28 and square of 3 is 09
So 53^2=2809
Here the square of the difference from 50 comes out to be a 3-digit number. So add the hundredth digit of the square to the sum obtained by adding or subtracting from 25.
For example: if you have to find square of 63, the difference from 50 comes out to be 13 and 13^2=169, so you have to add 1(hundredth place digit) to 25+13 and 25+13+1=39.
So 63^2=3969
If you have to find 34^2, the difference from 50 is (-16), 25-16=9 and (-16)^2=256, so we have to add 2 of 256 to 9(25-16), and we get 9+2=11,
So 34^2=1156
Here you have to check the difference from 100 and add or subtract double the difference of that number to 100, and by the side of this number you have to write the square of the difference.
For example: if you have to calculate square of 104, the difference from 100 is 4, 4x2+100, gives me 108, now 4^2=16,
So 104^2=10816
If you have to calculate square of 92, the difference from 100 is; so 100-2(8)=84, and (-8)^2=64.
So 92^2=8464
Here you have to check the difference from 100,and add or subtract that difference with 100 and along with that add the hundredth digit of the square of the difference to that sum and along with that write the unit’s and tenth of the square.
For example: if you have to calculate square of 114, the difference from 100 and 114-100=14 and 14^2=196, so adding double of the 14 and 1(hundredth place of 196) to 100, we get 100+2(14)+1=129 and putting it with 96,
So 114^2=12996
If we have to calculate square of 87, the difference from 100 is (-13), and (-13)^ 2=169, so adding double of (-13) and 1(hundredth place of 169), we get 100+2(-13)+1=75,
So 87^2=7569
- Square of any number from 40 to 60
Check the difference from 50 and add or subtract it from 25 and by the side of this number you have to write the square of that difference in 2 digits only (in case of 1, write 01).
For example: if you have to find square of 43
Difference from 50, i.e. 43 is 7 less than 50. So subtract 7 from 25, and you will get 18 and square of (-7) is 49.
So 43^2 = 1849
If you have to find square of 53,
Difference from 50 is 3, so adding 3 to 25, you will get 28 and square of 3 is 09
So 53^2=2809
- Square of any number from 26 to 40 and 61 to 75
Here the square of the difference from 50 comes out to be a 3-digit number. So add the hundredth digit of the square to the sum obtained by adding or subtracting from 25.
For example: if you have to find square of 63, the difference from 50 comes out to be 13 and 13^2=169, so you have to add 1(hundredth place digit) to 25+13 and 25+13+1=39.
So 63^2=3969
If you have to find 34^2, the difference from 50 is (-16), 25-16=9 and (-16)^2=256, so we have to add 2 of 256 to 9(25-16), and we get 9+2=11,
So 34^2=1156
- Square of any number from 90 to 110
Here you have to check the difference from 100 and add or subtract double the difference of that number to 100, and by the side of this number you have to write the square of the difference.
For example: if you have to calculate square of 104, the difference from 100 is 4, 4x2+100, gives me 108, now 4^2=16,
So 104^2=10816
If you have to calculate square of 92, the difference from 100 is; so 100-2(8)=84, and (-8)^2=64.
So 92^2=8464
- Square of any number from 76 to 89 and 111 to 125
Here you have to check the difference from 100,and add or subtract that difference with 100 and along with that add the hundredth digit of the square of the difference to that sum and along with that write the unit’s and tenth of the square.
For example: if you have to calculate square of 114, the difference from 100 and 114-100=14 and 14^2=196, so adding double of the 14 and 1(hundredth place of 196) to 100, we get 100+2(14)+1=129 and putting it with 96,
So 114^2=12996
If we have to calculate square of 87, the difference from 100 is (-13), and (-13)^ 2=169, so adding double of (-13) and 1(hundredth place of 169), we get 100+2(-13)+1=75,
So 87^2=7569