Simplify radicals by extracting perfect square, cube, or higher-power factors. Get exact radical form, decimal value, and clear steps.
To simplify √72, factor 72 as 36 × 2. Since √36 = 6, the simplified radical is 6√2.
√72 simplified exactly
- Find the largest perfect-power factor.
- Take that factor outside the radical.
- Leave the remaining factor inside the radical.
All calculations run locally in your browser. Your entered values are not sent to an external service.
How to Use the Simplify Radical Calculator
Select the root index, enter the radicand, and choose Simplify Radical. The calculator searches for the largest perfect-power factor that can come out of the radical.
- Use square root for expressions like √72.
- Use cube root for expressions like ∛54.
- Check the exact form before using the decimal approximation.
Radical Simplifying Rule
A radical is simplified by splitting the radicand into a perfect-power factor and the remaining factor.
For cube roots, the same idea uses perfect cubes. For example, ∛54 = ∛(27 × 2) = 3∛2.
Simplify Radical Examples
√200
200 = 100 × 2, so √200 = 10√2.
∛54
54 = 27 × 2, so ∛54 = 3∛2.
√18
18 = 9 × 2, so √18 = 3√2.
Common Radical Mistakes
Leaving a perfect-square factor inside the radical
Always look for the largest perfect square, not just the first factor you notice.
Using decimal-only answers
For algebra, the exact radical form is usually preferred over a rounded decimal.
Simplifying a negative square root as a real number
Negative square roots are not real numbers. Odd roots such as cube roots can have negative real answers.
Simplify Radical Calculator FAQs
What does it mean to simplify a radical?
It means to move any perfect-power factor outside the radical while keeping the exact value unchanged.
Does this simplify cube roots?
Yes. Choose cube root to extract perfect cube factors.
Is 6√2 exact?
Yes. 6√2 is the exact simplified form of √72.
How is this different from a square root calculator?
A square root calculator usually gives a decimal. A radical simplifier keeps the exact algebraic form when possible.
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Reviewer
This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.