Root Calculator
Calculate square roots, cube roots, and nth roots with precision. Our calculator provides step-by-step solutions, root tables, and verification of results. Perfect for mathematics, engineering, and scientific calculations.
Example Calculations
Square Roots
Cube Roots
Nth Roots
Root Rules and Properties
Basic Definitions
- Square Root: √x = x^(1/2)
- Cube Root: ∛x = x^(1/3)
- Nth Root: ⁿ√x = x^(1/n)
- Key Properties:
- • (√x)² = x
- • (∛x)³ = x
- • (ⁿ√x)ⁿ = x
- • √(a × b) = √a × √b (when a,b ≥ 0)
Advanced Rules
- Product Rule: ⁿ√(a × b) = ⁿ√a × ⁿ√b
- Quotient Rule: ⁿ√(a ÷ b) = ⁿ√a ÷ ⁿ√b
- Power Rule: ⁿ√(a^m) = (ⁿ√a)^m
- Root of Root: ᵐ√(ⁿ√a) = ^(m×n)√a
Applications of Roots
Mathematics
- • Solving polynomial equations
- • Simplifying radical expressions
- • Geometric calculations (diagonals, etc.)
- • Coordinate geometry (distance formula)
Physics & Engineering
- • Wave equations and harmonics
- • Structural calculations
- • Fluid dynamics
- • Electrical circuit analysis
Real-world Applications
- • Financial calculations (compound interest)
- • Computer graphics (vector normalization)
- • Statistics (standard deviation)
- • Machine learning algorithms