Your result
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Enter your values, then click Calculate result.How this calculator helps
Find a real cube or higher-degree root with an integer degree, signed odd-root handling and a power reconstruction check. The radicand is the number under the root, and the degree is the positive integer defining the power to reverse. This page accepts degrees two through one hundred and finite radicands within ±10¹². A cube root uses degree three, a fourth root degree four. The numeric field does not parse expressions such as 2^12; enter their evaluated value before calculating.
How to use it
- 1
Select the correct input roles for nth root calculator and enter the values described below. The demonstration defaults illustrate the method; they are not independently verified personal measurements or live market data.
- 2
Review negative odd roots and the original source record. Match units, signs and the chosen mode before submitting, rather than relying on a familiar-looking default number.
- 3
Click Calculate result to submit the current fields. Editing an input preserves the prior submitted output until you calculate again; the pending-change message distinguishes that saved output from the new values.
- 4
Check the labeled output against the worked example and independent verification steps. Review scope and precision before using the result in another document, and keep the complete input basis with a copied answer.
Formula and methodology
For degree n, a real root r satisfies rⁿ=x. Use sign(x)×|x|^(1/n) for odd negative roots; negative even radicands have no real root.
The calculator applies the displayed arithmetic to the values entered on this device. It does not silently load a local tax rate, currency conversion or commercial assumption.
Worked calculation example
The cube root of −27 is −3 because (−3)³=−27. The fourth root of 81 is the principal nonnegative value 3 because 3⁴=81. Although −3 also solves r⁴=81, the principal even root is nonnegative. A fourth root of −81 has no real value and produces a clear domain message rather than a guessed complex result.
How to interpret your result
Even powers are nonnegative for real inputs. A negative radicand therefore has no real even-degree root and is rejected. For a positive radicand, this page returns the nonnegative principal even root, not both solutions to a polynomial equation. Solving r⁴=81 as an equation is a different question from evaluating the principal fourth-root function at 81.
For different inputs or formulas, use Square Root Calculator; Quadratic Equation Calculator; Logarithm Calculator.
Related questions this calculator covers
- cube rooting calculator
- cube root calculator
- root calculator
Scenario comparison
| Scenario | What it shows |
|---|---|
| Cube | 125 with degree three gives 5. |
| Odd sign | −32 with degree five gives −2. |
| Zero | degree seven of zero gives zero. |
Common mistakes to avoid
- Confusing the degree with an exponent applied directly.
- Expecting negative real roots for a negative even radicand.
- Reading a principal even root as the complete equation solution set.
Raise the returned root to the degree independently. Check a perfect power such as 2⁵=32, a negative odd power and the zero boundary. For a positive input, squaring a degree-two result should agree with the protected separate square-root worksheet within rounding. The reconstruction validates arithmetic without making rounded output an exact symbolic answer.
Authoritative reference. Method and scope reviewed on 5 October 2026. SolvePilot provides the original worked example and bounded browser implementation. Editorial and arithmetic review by Mohammad Qasim does not certify user measurements, a real contract or an individual professional decision. The reference supplies method, unit or source-record context; it does not approve this implementation or its inputs.What can affect the result?
Radicand and degree
The radicand is the number under the root, and the degree is the positive integer defining the power to reverse. This page accepts degrees two through one hundred and finite radicands within ±10¹². A cube root uses degree three, a fourth root degree four. The numeric field does not parse expressions such as 2^12; enter their evaluated value before calculating.
Negative odd roots
An odd power preserves the sign of its base, so a negative radicand has a negative real odd-degree root. The implementation evaluates the magnitude first and reapplies the sign rather than passing a negative base to a fractional-power expression that may return an invalid numeric result. For example, degree five of −32 returns −2, because multiplying five negative factors gives a negative product.
Principal even roots
Even powers are nonnegative for real inputs. A negative radicand therefore has no real even-degree root and is rejected. For a positive radicand, this page returns the nonnegative principal even root, not both solutions to a polynomial equation. Solving r⁴=81 as an equation is a different question from evaluating the principal fourth-root function at 81.
Reconstruction check
The supporting row raises the computed root to the entered degree. It should approximately recover the radicand, allowing floating-point and display rounding. Near zero or at high degrees, compare the reconstructed value with the scale of the original input instead of demanding identical decimal text. Scientific notation preserves a nonzero small result that would disappear under fixed decimal rounding.
Scope and precision
This worksheet returns a real numeric root, not an exact simplified radical, symbolic expression or complete complex root set. Zero has root zero for every supported degree. One has principal root one. High-degree roots of positive values move toward one, which is mathematically expected rather than a calculation failure. Copy both degree and radicand with the result; omitting degree leaves the operation ambiguous.
Privacy and browser processing
Values entered on this page are processed in the current browser session. SolvePilot does not require an account and does not receive the values entered into the calculator. Refreshing or closing the page clears the working values unless the browser itself restores a previous session. Avoid entering identifying or account information because the calculation needs summary values only.
Accuracy and verification
Accuracy depends first on input quality. Confirm definitions, scales, dates and source information before entering a value. Keep an independent record of any result used for planning because this page does not create an official statement or retain a calculation history.
Limits of this estimate
This worksheet returns a real numeric root, not an exact simplified radical, symbolic expression or complete complex root set. Zero has root zero for every supported degree. One has principal root one. High-degree roots of positive values move toward one, which is mathematically expected rather than a calculation failure. Copy both degree and radicand with the result; omitting degree leaves the operation ambiguous.
Sources and review information
Frequently asked questions
What is a cube root?＋
It is the real number whose third power equals the radicand. Degree three supports negative inputs as well as nonnegative ones.
Why reject a negative fourth root input?＋
No real number raised to an even power is negative. Complex roots exist, but this page intentionally returns real roots only.
Does it return both even roots?＋
No. It evaluates the principal nonnegative root. An equation involving an even power can have both signs as solutions.
Can the root degree be fractional?＋
No. This worksheet requires an integer degree from two through one hundred.
Are radical answers exact?＋
The displayed values are numerical approximations, even when the true root is irrational. The power row helps check the arithmetic.