Find Perfect Squares Mentally with this Trick
Brett Berry

My favorite trick (or property) of squares is that the number between the the squares of two consecutive numbers is those two numbers added together.

Example: 6² is 36, 6+7=13, 7² is 49, or 36+13!

One note is to remember to “double-count” if you are going up more than one number.

Example 6² is 36, 9² is 81, 36 + (6+7) +(7+8) +(8+9)=81

Its great if you use multiples of 10

To get 83² take 80²=6,400 Add 80+81+81+82+82+83 which gets you 6,889.

This may be easier to calculate in your head depending on how you mentally “see” things.