Root Calculator

In mathematics, the general root

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:

1. Estimate a number b.

2. Divide a by b. If the number c returned is precise to the desired decimal place, stop.

3. Average b and c and use the result as a new guess.

4. 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:

1. Estimate a number b.

2. Divide a by bⁿ⁻¹. If the number c returned is precise to the desired decimal place, stop.

3. Average: [b × (n − 1) + c] / n.

4. Repeat step two.