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The Root of it All


Morgan V Courage The sqrt button on the free Microsoft calculator references one of the earliest known calculations by man, the square root. This calculation is the corner stone for human logic, farmers, finance, construction, engineers, scientists, doctors, optometrists, nurses, pharmacists, architects, surveyors, cartographers, statisticians,educators, economists and even lawyers. The modern world thrives on a simple calculation written on a clay tablet by Babylonians around 1700 BC. But how many in this modern world can calculate a square root with pen, paper and the mind?


The National Institute of Standards and Technology (NIST) describe an algorithm for the manual method of calculating square roots by hand. The steps of this algorithm are best described by an example. Using a large random number, 60516, set up a “division” with the number under the radical. Mark off pairs of digits, starting from the decimal point and working left. The decimal point is a period (.) and commas (,) mark pairs of digits.

√6,05,16. Look at the leftmost digit(s) (6 in this case). What is the largest number whose square is less than or equal to it? It is 2, whose square is 4. Write 2 above and write the square below and subtract.

2 √6,05,16. -4 2

Now bring down the next two digits (05). The next divisor is double the number on top (2x2=4) and some other digit in the unit’s position (4_).

2 √6,05,16. -4 4_) 205

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