Here's another one:
squaring numbers ending in 5, eg. 75:
Take the digit in front of the 5 (here: 7) and multiply it by its successor (here: 7+1=8), giving, in this example, 7x8=56, then add digits 25, giving 5625.
75 squared is 5625.
And:
74 squared is 75 squared - 74 -75
76 squared is 75 squared + 75 + 76
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