Radical Simplifier
Simplify √n by extracting the largest perfect-square factor: √n = a√b.
About Radical Simplifier
To simplify a radical, find the prime factorization of the number under the radical. For each prime factor, extract groups of size equal to the root index. For example, √72 = √(36·2) = 6√2, because 72 = 2³·3² and we extract one pair of 3s and one pair of 2s.
Formula
Radical simplification
ⁿ√(a^n · b) = a · ⁿ√b
- a
- Extracted coefficient
- b
- Remaining radicand
- n
- Root index
Worked example
With the default values below, Radical Simplifier returns Simplified Form of 6√2. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number under radical (n)minimum 1
- 72
- Root indexaccepts 2–10
- 2
Results
- Simplified Form
- 6√2
- Coefficient Outside
- 6
- Remaining Radicand
- 2
- Decimal Value
- 8.48528137
Step by step
- 1Values used
- 2Radical simplification
- 3Simplified Form= 6√2
- 4Coefficient Outside= 6
- 5Remaining Radicand= 2
- 6Decimal Value= 8.48528137
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is a perfect square factor?
A perfect square factor is a factor of the radicand that is itself a perfect square (like 4, 9, 16, 25...). Extracting it simplifies the radical.
Can this simplify cube roots?
Yes — set the root index to 3. For cube roots, it extracts perfect cube factors.