Method 1: Numbers Near 100
A quick way to find the square of numbers close to 100.
Example: Find 106²
1
Find the difference from 100
The number is
106
. The difference is 106 - 100 = +6
.2
Square the difference
The square of the difference
6
is 36
. This will be the last two digits of your answer.3
Add the difference to the original number
Add the difference
+6
to the original number 106
: 106 + 6 = 112
. This will be the first part of your answer.Result
Combine the two parts:
112
and 36
gives you 11236.Example with Carry-over: Find 112²
1
Find the difference from 100
The number is
112
. The difference is 112 - 100 = +12
.2
Square the difference (with carry-over)
The square of
12
is 144
. We need only two digits, so we keep 44
and carry over the 1
.3
Add difference to original number
Add the difference
+12
to the original number 112
: 112 + 12 = 124
.4
Add the carry-over
Add the carry-over
1
to the result from the previous step: 124 + 1 = 125
. This is the first part of the answer.Result
Combine the parts:
125
and 44
gives you 12544.Method 2: Numbers Near 50
Similar to the 100-base method, but with a twist. The base for addition/subtraction becomes 25.
Example (Above 50): Find 56²
1
Find the difference from 50
The number is
56
. The difference is 56 - 50 = +6
.2
Square the difference
Square of
6
is 36
. These are the last two digits.3
Add the difference to 25
The key step: add the difference
+6
to the magic number 25
: 25 + 6 = 31
. This is the first part of the answer.Result
Combine the parts:
31
and 36
gives you 3136.Example (Below 50): Find 42²
1
Find the difference from 50
The number is
42
. The difference is 42 - 50 = -8
.2
Square the difference
Square of
-8
is 64
. These are the last two digits.3
Subtract the difference from 25
Subtract the difference's absolute value (
8
) from the magic number 25
: 25 - 8 = 17
. This is the first part.Result
Combine the parts:
17
and 64
gives you 1764.