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Formulas That Work is a Hub for Land surveyor support for sharing common or not so common calculation shortcuts and formulas for survey data calculations. Share your Surveyor Math Formulas and Computational Tricks Here GEO Ambassador

Land surveyors are constantly crunching numbers in their head.  But if you are like me, math is "work" part of surveying.

To square any two-digit number X, decide what number N it will take to raise or lower X to P, the nearest multiple of 10. Add the opposite of N to X to get Q, multiply P times Q, and add N^2 to the result. For instance:

`67 * 67 = (67 + 3) * (67 - 3) + (3 * 3) =  70      *  64      +  9      = 4489`

The hard part is 70 * 64, but if you teach yourself to ignore the zero at the end of the 70 and multiply from left to right, it sounds like this:

"Seven sixes make forty-two, times ten makes four hundred and twenty. Seven fours make twenty-eight, plus four hundred and twenty makes four hundred and forty-eight, times ten makes forty-four hundred and eighty, plus three squared--that's nine--makes forty-four hundred and eighty-nine."

Presto, you've figured out the answer in less time than it takes to say it. Note: don't be discouraged if you forget what number you needed to add at the end, or what number you were originally squaring; they're going to drop out of your short-term memory storage until you practice enough.

Here's an easier one, 52 * 52:

`52 * 52 = (52 + 2) * (52 - 2) + (2 * 2) =  54      *  50      +  4      = 2704`

Numbers ending in 4 and 6 are the hardest, because you've got to add 16.

`86 * 86 = (86 + 4) * (86 - 4) + (4 * 4) =  90      *  82      +  16     = 7396`

Numbers ending in 1 are easy:

`71 * 71 = (71 + 1) * (71 - 1) + (1 * 1) =  72      *  70      +  1      = 5041`

... and numbers ending in 5 are trivial:

`45 * 45 = (45 + 5) * (45 - 5) + (5 * 5) =  50      *  40      +  25     = 2025`

This is math that the average fourth-grader can handle ... can you?

Do you have any heady-math tricks you'd like to share with the community?

This is a tip from an insightful blogger that I read pretty regularly, Kent Brewster

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