Free · Arithmetic calculators ➗

Nonnegative Cube and Variable-Degree Roots

Nonnegative Cube and Variable-Degree Roots. Evaluate a real power or principal root, with reverse inputs where a unique solution exists.

  • Formula & worked example
  • Private in your browser
  • No signup
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

Principal root = 2.

root^degree = radicand

Worked example

Enter these known values and leave the other values blank.

Nonnegative radicand
8
Principal root
2

Assumptions and limitations

  • Arithmetic uses 64 significant decimal digits, with separate rounding for displayed results. Very large integer arithmetic is not an exact arbitrary-length integer service.
  • The captured radicand domain is nonnegative. This tool preserves that domain and does not calculate negative real cube roots or complex roots.
  • The root degree must be nonzero. The calculated root is the nonnegative principal real root; solving for degree uses logarithms and can be indeterminate for radicand or root equal to zero or one.
  • A negative degree gives a reciprocal root and requires a positive radicand. The default degree can be edited; unlock the degree field if required.

Common questions

Can I enter the result to calculate a missing input?

The retained inverse rules solve from sufficient known inputs. Roots and inverse trigonometric functions use principal values; indeterminate inputs do not have a unique solution.

References

Bookify rejects undefined zero powers or zero root/exponent denominators and validates real-valued powers while preserving the captured equations and inverse rules.

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