Root Calculator
Calculate square roots, cube roots, and any nth root of numbers. Detect perfect roots and verify your calculations.
Root Calculator
About Roots & Radicals
A root is the inverse operation of an exponent. Finding the nth root of a number means finding a value that, when raised to the nth power, equals the original number.
Types of Roots
- Square Root (√): Most common, finds x where x² = n
- Cube Root (∛): Finds x where x³ = n
- Fourth Root: Finds x where x⁴ = n
- nth Root: Finds x where xⁿ = n
Perfect Roots
- Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
- Perfect cubes: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000...
- Perfect fourth powers: 1, 16, 81, 256, 625, 1296...
Properties of Roots
- √(ab) = √a × √b
- √(a/b) = √a / √b
- ⁿ√(aᵐ) = a^(m/n)
- Even roots of negative numbers are undefined in real numbers
- Odd roots of negative numbers are negative
Applications
- Geometry: Finding side lengths in right triangles
- Physics: Calculating velocities and accelerations
- Engineering: Stress and strain calculations
- Finance: Compound interest and growth rates
- Statistics: Standard deviation calculations