Using the Root Calculator
The answer is the real number that produces the original value when raised to the selected degree. For a negative radicand, an odd degree can give a negative real root, while an even degree cannot.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- Radicand
- 27
- Root degree
- 3
Example result
- Root
- 3
Method and assumptions
The nth root is the real number whose nth power is the radicand.
Check signs and valid inputs
Powers, roots and logarithms have restrictions that ordinary addition does not. Zero, a negative base or a fractional exponent may change whether a real-number answer exists. Read the method's supported domain and keep parentheses around negative values where the input is an expression. A rejected input may indicate a mathematical restriction rather than a formatting problem.
Common question
Why does the cube root of a negative number work?
Multiplying an odd number of negative factors gives a negative result. Three factors of −3 give −27, so the real cube root of −27 is −3.
Guide updated .