Squaring a 2-digit Number Ending in 4:
Take a 2-digit number ending in 4 as d4; where d is the first digit. For example, 34 will be d4; where d=3 (the first digit).
d4^2 = (d0 + 4)^2 = (d^2 * 100) + (8 * d0) + 16
Or:
d4^2 = [(d^2 * 10) + (8 * d) + 1] & 6
So, to square a 2-digit number ending in 4, take 10 times of the square of its first digit, add 1 plus 8 times of the first digit to it, and append a 6 to the result.
Example 1: Take 24 as the number to calculate its square:
10 * 2^2 (10 times of the square of the first digit)
+
1 + (8 * 2) (add 1 plus 8 times of the first digit)
&
6 (append a 6),
so 24^2 = 40 + 17 & 6 = 576
Example 2: Take 94 as the number to calculate its square:
10 * 9^2 (10 times of the square of the first digit)
+
1 + (8 * 9) (add 1 plus 8 times of the first digit)
&
6 (append a 6),
so 94^2 = 810 + 73 & 6 = 8836
Squaring a 2-digit Number Ending in 5:
This trick is pretty simple. Choose a 2-digit number ending in 5; multiply the first digit by the next consecutive number and append a 25 to the end of it.
Example 1: 25^2 = (2 * 3) & 25 = 625
Example 2: 85^2 = (8 * 9) & 25 = 7225
Squaring a 2-digit Number Ending in 6:
To square a 2-digit number ending in 6, take 10 times of the multiplication of the first digit by the next consecutive number, add 3 plus 2 times of the first digit to it, and append a 6 to the result.
Example 1: Take 26 to calculate its square:
10 * (2 * 3) (10 times of the multiplication of the first digit by the next consecutive number)
+
3 + (2 * 2) (add 3 plus 2 times of the first digit)
&
6 (append a 6)
so 26^2 = (60 + 7) & 6 = 676
Example 2: Take 86 to calculate its square:
10 * (8 * 9) (10 times of the multiplication of the first digit by the next consecutive number)
+
3 + (2 * 8) (add 3 plus 2 times of the first digit)
&
6 (append a 6)
so 86^2 = (720 + 19) & 6 = 7396
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