Take the digits before the five, multiply by the next number up, and stick 25 on the end. Twenty five squared is 6 followed by 25, because two times three is six.
35 squared: take the 3, multiply by 4, get 12, then append 25. The answer is 1225. 85 squared: 8 times 9 is 72, so 7225.
It is not a coincidence. Any number ending in five can be written as ten times something, plus five. Call the something n, so the number is 10n plus 5.
Square it and you get 100n squared plus 100n plus 25, which factors to 100 times n times (n plus 1), plus 25. The hundred means whatever n times (n plus 1) comes to sits in the hundreds column and above, and the 25 sits underneath it untouched.
So the rule is the algebra read aloud. This is worth doing with any shortcut you are told to memorise: find the line of algebra it came from, and you will never have to remember which cases it fails on.
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