This is the last part of Squaring a 2-digit Number Ending in X. As mentioned in the first part, practice, and try to do the following tricks as fast as possible as they will be used in some fundamental tricks in the future posts.
Squaring a 2-digit Number Ending in 7:
This trick has the same pattern as "Squaring a 2-digit Number Ending in 6".
To square a 2-digit number ending in 7, take 10 times of the multiplication of the first digit by the next consecutive number, add 4 plus 4 times of the first digit to it, and append a 9 to the result.
Example 1: Take 27 to calculate its square:
10 * (2 * 3) (10 times of the multiplication of the first digit by the next consecutive number)
+
4 + (4 * 2) (add 4 plus 4 times of the first digit)
&
9 (append a 9)
so 27^2 = (60 + 12) & 9 = 729
Example 2: Take 87 to calculate its square:
10 * (8 * 9) (10 times of the multiplication of the first digit by the next consecutive number)
+
4 + (4 * 8) (add 4 plus 4 times of the first digit)
&
9 (append a 9)
so 87^2 = (720 + 36) & 9 = 7569
Squaring a 2-digit Number Ending in 8:
This trick has the same pattern as "Squaring a 2-digit Number Ending in 6" and 7.
To square a 2-digit number ending in 8, take 10 times of the multiplication of the first digit by the next consecutive number, add 6 plus 6 times of the first digit to it, and append a 4 to the result.
Example 1: Take 28 to calculate its square:
10 * (2 * 3) (10 times of the multiplication of the first digit by the next consecutive number)
+
6 + (6 * 2) (add 6 plus 6 times of the first digit)
&
4 (append a 4)
so 28^2 = (60 + 18) & 4 = 784
Example 2: Take 68 to calculate its square:
10 * (6 * 7) (10 times of the multiplication of the first digit by the next consecutive number)
+
6 + (6 * 6) (add 6 plus 6 times of the first digit)
&
4 (append a 4)
so 68^2 = (420 + 42) & 4 = 4624
Squaring a 2-digit Number Ending in 9:
To square a 2-digit number ending in 9, take the next number y which ends in zero. For example, to square 39, take y = 40. Then calculate y^2 - (2 * y) + 1.
Example 1: Take 49 to calculate its square. In this example y = 50:
49^2 = 50^2 - (2 * 50) + 1 = 2500 - 100 + 1 = 2401
Example 2: Take 89 to calculate its square. In this example y = 90:
89^2 = 90^2 - (2 * 90) + 1 = 8100 - 180 + 1 = 7921
In the above example, to compute 8100 - 180 quickly, you may think like:
8100 - 180 = 8100 - 200 + 20 = 7900 + 20 = 7920.
Again, learn to apply the tricks of "Squaring a 2-digit Number Ending in X" quickly; practice and practice; the Germans say: Übung macht den Meister!