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 1:
Take a 2-digit number ending in 1 as X. X^2 will be: (X-1)^2 + 2 * (X-1) + 1.
Example 1: Take 31 as the number to calculate its square:
31 - 1 = 30
(30^2) + (2 * 30) + 1 = 900 + 60 + 1 = 961
So 31^2 = 961
Example 2: Take 81 as the number to calculate its square:
81 - 1 = 80
(80^2) + (2 * 80) + 1 = 6400 + 160 + 1 = 6561
So 81^2 = 6561
Squaring a 2-digit Number Ending in 2:
Take a 2-digit number ending in 2.
Multiply square of its first digit by 10, add four times of its first digit to it, and put a 4 at its end.
Example 1: Take 42 as the number to calculate its square:
(4^2) * 10 (multiply square of its first digit by 10)
+
4 * 4 (four times of its first digit)
& 4 (put a 4 at its end):
((16 * 10) + 16) & 4:
1764
So 42^2 = 1764
Example 2: Take 92 as the number to calculate its square:
(9^2) * 10 (multiply square of its first digit by 10)
+
4 * 9 (four times of its first digit)
& 4 (put a 4 at its end):
((81 * 10) + 36) & 4:
8464
So 92^2 = 8464
Squaring a 2-digit Number Ending in 3:
Take a 2-digit number ending in 3.
Multiply square of its first digit by 10, add six times of its first digit to it, ans put a 9 at its end.
Example 1: Take 43 as the number to calculate its square:
(4^2) * 10 (square of its first digit by 10)
+
6 * 4 (six times of its first digit)
& 9 (put a 9 at its end):
((16 * 10) + 24) & 9:
1849
So 43^2 = 1849
Example 2: Take 93 as the number to calculate its square:
(9^2) * 10 (multiply square of its first digit by 10)
+
6 * 9 (six times of its first digit)
& 9 (put a 9 at its end):
((81 * 10) + 54) & 9:
8649
So 93^2 = 8649
[continued ...]