Radical Calculator
Simplify an integer square, cube, or higher root by extracting complete powers, and also report its decimal approximation. Negative radicands are accepted only with odd indexes. This page covers “under root 20”.
How to use the Radical Calculator
Enter an integer radicand and a whole-number root index from 2 through 20.
Review real versus complex domain, radicand sign, whole-number index range, and displayed decimal rounding.
Read exact simplified form, decimal approximation, outside factor, and remaining radicand.
Formula
Prime exponents are divided by the root index: each quotient moves outside the radical and each remainder stays inside. The approximation is x^(1/n) in the real domain.
Example
The square root of 72 simplifies exactly to 6√2 and is approximately 8.4852813742.
Assumptions and limitations
- Exact factor extraction is limited to safe integer radicands; complex roots and symbolic expressions are not supported.
- Radical Calculator treats the entered values as estimates and does not infer missing project, account, or personal details.
- Calculations retain working precision except where the cited method requires an intermediate rounding step; displayed values are then formatted separately. Source rules and dated rates must be rechecked when they change.
Sources
- OpenStax: College Algebra 2eAlgebraic, ratio, radical, equation, and function formulas. Reviewed 2026-08-14.
- OpenStax: Elementary Algebra 2eOfficial formula, rate, or program guidance used by this calculator. Reviewed 2026-08-14.
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Frequently asked questions
How does the Radical Calculator work?
Prime exponents are divided by the root index: each quotient moves outside the radical and each remainder stays inside. The approximation is x^(1/n) in the real domain.
What information should I enter in the Radical Calculator?
Enter an integer radicand and a whole-number root index from 2 through 20, then verify real versus complex domain, radicand sign, whole-number index range, and displayed decimal rounding.
What should I verify before using this Radical Calculator result?
Exact factor extraction is limited to safe integer radicands; complex roots and symbolic expressions are not supported.
Reviewed 2026-08-14 · integer-factorization-v2 · content-2026-08-14 · Trusty Calculator Editorial Team