Root Calculator

About Roots

In mathematics, the n-th root of a number a is another number b that when multiplied by itself n times equals a. In equation format: n√a = b, b^n = a.

Common roots include square root (n=2) and cube root (n=3).

Estimating a Root

To estimate √a:

1. Estimate a number b
2. Divide a by b. If precise, stop.
3. Average b and c (result of division) as new guess
4. Repeat step two

EX: √27 → Guess 5.125, 27/5.125=5.268, (5.125+5.268)/2=5.197, 27/5.197=5.195, (5.195+5.197)/2=5.196

Estimating an n-th Root

To estimate n√a:

1. Estimate a number b
2. Divide a by b^(n-1). If precise, stop.
3. Average: [b × (n-1) + c] / n
4. Repeat step two

EX: 8√15 → Guess 1.432, 15/1.432^7=1.405, (1.432×7+1.405)/8=1.388, 15/1.388^7=1.403, (1.403×7+1.388)/8=1.402