ClarityHow to use this tool
- Enter radicand, root degree.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
The method, explained
The real nth root of nonnegative x is x^(1/n). For negative x and odd n, take −(|x|^(1/n)); even roots of negative values have no real result.
Using radicand = -125, root degree = 3, the result is -5. Change these example inputs to match your task; use the method above to check each step.
Understanding your result
The radical notation uses the principal nonnegative root for a nonnegative input. Solving x⁴ = a as an equation is a different task and can have two real roots.
What to keep in mind
Returns the real root only, not all complex roots. Non-integer root degrees are unsupported. Finite-precision arithmetic is used. Check the domain and the stated convention before using an approximation.
Common questions
Does a fourth root return both signs?
The radical notation uses the principal nonnegative root for a nonnegative input. Solving x⁴ = a as an equation is a different task and can have two real roots.
How can I check the result?
The real nth root of nonnegative x is x^(1/n). For negative x and odd n, take −(|x|^(1/n)); even roots of negative values have no real result. The worked example uses editable inputs. Calculations run on your device; no external API or account is required.
Methodology maintained by ClarityKit. How these tools are built and checked.