Root Calculator

Professional root calculator for square roots, cube roots, nth roots and radical expressions

Square Root Result

√ 25 = 5
Input Number: 25
Square Root: 5
Perfect Square: Yes
Decimal Form: 5.000000

Calculation Steps:

1. Enter a number to see square root calculation steps

Cube Root Result

∛3 27 = 3
Input Number: 27
Cube Root: 3
Perfect Cube: Yes
Decimal Form: 3.000000

Calculation Steps:

1. Enter a number to see cube root calculation steps

Nth Root Result

ⁿ√5 32 = 2
Input Number: 32
Root Index: 5
Nth Root: 2
Decimal Form: 2.000000

Formula:

ⁿ√x = x^(1/n)
1. Enter values to see nth root calculation steps
Real part + Imaginary part

Complex Roots

1 + i
Primary Root
Input: 1 + i
Root Index: 2
Magnitude: √2
Number of Roots: 2

All Roots:

1. Enter complex number to see all roots

How to Use the Root Calculator

Our comprehensive root calculator provides four powerful tools for calculating different types of roots with step-by-step solutions:

√ Square Root Calculator

Calculate square roots with multiple output formats including simplified radical form, decimal approximation, and estimation methods. Supports both positive and negative roots with customizable precision levels. Perfect for basic algebra, geometry, and practical calculations.

∛ Cube Root Calculator

Find cube roots of positive and negative numbers with exact and approximate solutions. Automatically detects perfect cubes and provides simplified forms when possible. Essential for volume calculations, engineering applications, and advanced mathematics.

ⁿ√ Nth Root Calculator

Calculate any nth root (4th root, 5th root, etc.) up to the 20th root with high precision. Uses the mathematical relationship x^(1/n) for accurate calculations. Useful for advanced algebra, calculus, and specialized mathematical applications.

ℂ Complex Root Calculator

Find all complex roots of complex numbers using polar and rectangular forms. Calculates multiple roots based on the fundamental theorem of algebra. Displays results in both rectangular (a + bi) and polar (r∠θ) formats for comprehensive analysis.

🌟 Key Features

• Multiple Root Types: Square, cube, nth, and complex roots
• High Precision: Up to 10 decimal places accuracy
• Perfect Root Detection: Identifies perfect squares, cubes, and nth powers
• Simplified Forms: Radical simplification and exact forms
• Step-by-Step Solutions: Detailed calculation processes
• Multiple Formats: Decimal, simplified, and complex number formats
• Educational Value: Perfect for learning root concepts and properties
• Professional Interface: Clean design for efficient calculations

Whether you're a student learning about radicals and roots, an engineer working with complex calculations, or anyone needing precise root calculations, our calculator provides the accuracy and educational insight you need.

Frequently Asked Questions

Square root finds a number that when multiplied by itself gives the original number (√25 = 5 because 5² = 25). Cube root finds a number that when cubed gives the original number (∛27 = 3 because 3³ = 27). Square roots have two solutions (±), while cube roots have one real solution.
To simplify square roots, factor the radicand into perfect square factors. For example, √72 = √(36 × 2) = √36 × √2 = 6√2. Our calculator automatically provides simplified radical forms when possible and shows the factorization process.
Even roots (square, 4th, 6th, etc.) of negative numbers result in complex numbers. Odd roots (cube, 5th, 7th, etc.) of negative numbers are real and negative. Our calculator handles both cases and can display complex results when appropriate.
Complex roots involve imaginary numbers and are used when finding roots of negative numbers (for even roots) or when working with complex numbers. They're essential in electrical engineering, signal processing, and advanced mathematics. Our calculator shows all complex roots in both rectangular and polar forms.
Our calculator uses high-precision algorithms with accuracy up to 10 decimal places. For perfect roots (perfect squares, cubes, etc.), results are exact. For irrational roots, we provide highly accurate approximations using advanced numerical methods like Newton's method for optimal precision.