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Free simplest radical form calculator. Simplify radicals (square roots, cube roots, nth roots) to their simplest form with step-by-step solutions. Perfect for algebra calculations and mathematics. Our calculator finds perfect nth power factors and extracts them to simplify any radical expression.
Last updated: February 2, 2026
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Simplified Form
6√2
Decimal Value
8.4853
Coefficient
6
Remaining Radicand
2
Analysis:
Simplified by extracting 6² = 36
The simplest radical form of √72 is 6√2. This is simplified by factoring out 6² = 36 from 72.
Example
√72 = 6√2
Extracts perfect square factors (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...)
Example
³√54 = 3³√2
Extracts perfect cube factors (1, 8, 27, 64, 125, 216...)
Example
⁴√16 = 2
Works for 4th roots, 5th roots, and higher order roots
Perfect squares
1, 4, 9, 16, 25, 36...
Automatically finds the largest perfect square factor
Method
Factor & Extract
Uses prime factorization to find perfect nth power factors
Conversion
Standard ↔ Simplest
Converts between standard and simplest radical forms
Simplifying √72 to simplest radical form:
Original
√72
Simplified
6√2
Our simplest radical form calculator uses perfect nth power factorization to simplify radicals. The calculation applies algebraic factorization principles to identify and extract perfect nth power factors (perfect squares, perfect cubes, etc.) from the radicand, reducing the radical to its simplest form.
√72 = √(36 × 2) = √36 × √2 (factor)√72 = 6 × √2 = 6√2 (extract)³√54 = ³√(27 × 2) = 3³√2 (cube root)Perfect nth powers extracted (result)The calculator finds the largest perfect nth power factor of the radicand, extracts it from under the radical, and multiplies it by any existing coefficient. The remaining radicand has no perfect nth power factors.
Shows factorization and extraction process for simplifying radicals
Simplifying radicals is based on the property that √(a × b) = √a × √b and ³√(a × b) = ³√a × ³√b. When a is a perfect nth power, we can evaluate its nth root exactly, leaving only the non-perfect factor under the radical. This process reduces the complexity of radical expressions and makes them easier to work with.
Need help with other algebra calculations? Check out our roots calculator and simplify square root calculator.
Get Custom Calculator for Your PlatformResult: √72 = 6√2
The radical is now in simplest form since 2 has no perfect square factors.
³√54
54 = 27 × 2
³√54 = 3³√2
√144
144 = 12²
√144 = 12
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