- Root
- 3
How it works
A principal root is one answer
The square-root result for 9 is 3, while the equation x² = 9 has two real solutions, 3 and −3. Use the root result as a function value, not as a complete equation solution list.
Understanding the root index and input value
The root index specifies which power would reproduce the entered value. A square root and a cube root therefore answer different questions about the same number. Review the real-number restrictions when the input is negative or the index is not a whole number. The calculator's root result should not be confused with listing every possible solution of a polynomial equation.
Nth root: formula and assumptions
Nth root = value ^ (1/n).
Negative values have real odd roots; even roots of negative values are complex and outside this mode.
Worked example
Using the Nth root example:
- Number
- 27
- Root degree
- 3
Nth root = value ^ (1/n).
Example result
Root: 3
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Can a negative number have a real root?
It has real odd roots, such as the cube root of −8 being −2. Even roots of negative values are not real.
Does the calculator list every complex root?
No. This mode returns the supported real root rather than the full set of complex roots.
Prepared by Finflo. See our methodology and editorial policy.