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Summary
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In mathematics, the general root, or the nth root of a number a is another number b that when multiplied by itself n times, equals a. In equation format:
n√a = b
bn = a
Estimating a Root
Some common roots include the square root, where n = 2, and the cubed root, where n = 3. Calculating square roots and nth roots is fairly intensive. It requires estimation and trial and error. There exist more precise and efficient ways to calculate square roots, but below is a method that does not require a significant understanding of more complicated math concepts. To calculate √a:
Estimate a number b
Divide a by b. If the number c returned is precise to the desired decimal place, stop.
Average b and c and use the result as a new guess
Repeat step two
Estimating an nth Root
Calculating nth roots can be done using a similar method, with modifications to deal with n. While computing square roots entirely by hand is tedious. Estimating higher nth roots, even if using a calculator for intermediary steps, is significantly more tedious. For those with an understanding of series, refer here for a more mathematical algorithm for calculating nth roots. For a simpler, but less efficient method, continue to the following steps and example. To calculate n√a:
Estimate a number b
Divide a by bn-1. If the number c returned is precise to the desired decimal place, stop. Average: [b × (n-1) + c] / n
It should then be clear that computing any further will result in a number that would round to 1.403, making 1.403 the final estimate to 3 decimal places.
