Quadratic Equation Solver (ax² + bx + c = 0)
About Root Calculator
The Comprehensive Radical & Square Root ($\sqrt{x}$) Calculator computes exact principal roots, radical simplifications (e.g. $\sqrt{72} = 6\sqrt{2}$), rationalized denominators, and complex roots for negative numbers ($i$).
How to Use Root Calculator
Step 1
Enter a number (positive or negative).
Step 2
Review the decimal approximation and exact simplified radical form ($a\sqrt{b}$).
Step 3
Inspect prime factorization and step-by-step extraction proof.
Step 4
Click "Copy Root".
Practical Use Cases for Root Calculator
Radical Simplification for Algebra & Geometry (Exact Form)
Simplify radical expressions into exact reduced radical forms ($a\sqrt{b}$) without rounding to approximate decimals.
Pythagorean Theorem & Distance Formula Calculations
Compute hypotenuse lengths ($c = \sqrt{a^2 + b^2}$) and Euclidean distances with step-by-step square factor extraction.
Input & Output Examples
Simplifying Square Root of 300
Number: `300`
Decimal: `17.320508...` | Exact Simplified Radical: `10√3` | Prime Factorization: `2² × 3 × 5²`
Key Features & Performance
- ✓Simplifies radicals into exact integer factor form $a\sqrt{b}$ by extracting perfect square prime factors.
- ✓Complex Root Engine: computes imaginary roots for negative numbers ($\sqrt{-25} = 5i$).
- ✓High-precision decimal evaluations up to 50 significant digits.
- ✓100% Client-Side math engine.
- ✓1-Click Copy exact radical expression & decimal.
Key Terminology & Definitions
Principal Square Root
The unique non-negative square root of a non-negative real number ($ hostility\sqrt{x} \ge 0$).
Radicand
The value or algebraic expression located beneath the radical symbol ($\sqrt{\text{radicand}}$).