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Free simplify square root calculator & radical calculator. Simplify square roots to radical form, find perfect square factors & decimal approximations. Our calculator uses factorization principles to provide accurate radical simplification for algebra, geometry, and mathematics education.
Last updated: February 2, 2026
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Enter a non-negative number to find √number
Simplified: 8 = 2² × 2
Simplification method
Perfect Square Factorization
Factor out largest perfect squares for maximum simplification
Perfect squares
1, 4, 9, 16, 25, 36, 49, 64...
Recognize and extract perfect square factors
Output formats
Radical + Decimal
Show both exact radical form and decimal approximation
Algebraic operations
√(a × b) = √a × √b
Apply square root properties for simplification
Mathematical properties
Factorization Rules
Use mathematical properties for accurate simplification
Radical types
Square Roots, Cube Roots
Simplify various types of radical expressions
For √8 (simplified):
Original
√8
Simplified
2√2
Decimal
2.828
Our simplify square root calculator uses factorization principles to find the largest perfect square factors and simplify radicals to their simplest form. The calculation applies mathematical properties of square roots to provide accurate radical simplification for algebra, geometry, and mathematical education.
√n = √(perfect square × remaining)√n = √(perfect square) × √(remaining)√n = coefficient × √(remaining)The process finds the largest perfect square that divides the number, then uses the property √(a × b) = √a × √b to separate the perfect square from the remaining factor.
Shows how to factor out perfect squares from square roots
Square root simplification is based on the fundamental properties of radicals and perfect squares. Perfect squares (1, 4, 9, 16, 25, etc.) have integer square roots, making them ideal factors to extract. The process uses the distributive property of square roots over multiplication to achieve maximum simplification.
Need help with other algebraic calculations? Check out our quadratic formula calculator and factoring calculator.
Get Custom Calculator for Your PlatformResult: √12 = 2√3
Simplified form: 2√3 ≈ 3.464 (decimal approximation).
√16
√16 = 4 (perfect square)
√7
√7 (already simplified)
Share it with others who need help with radical simplification
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