Root Calculator
Calculate nth roots including cube roots, fourth roots, and higher-order roots with step-by-step calculations and perfect power detection. Perfect for algebra and advanced mathematics.
Nth Root Calculator
Common Root Calculations
Click on these links to see instant calculations with common roots:
Nth Roots
An nth root of a number is a value that, when raised to the power n, gives the original number. Roots are the inverse operation of exponentiation.
Root Properties
ⁿ√(xy) = ⁿ√x × ⁿ√y
ⁿ√(x/y) = ⁿ√x / ⁿ√y
(ⁿ√x)ⁿ = x
ⁿ√(xᵐ) = x^(m/n)
Common Roots
| Root Type | Index (n) | Symbol | Example |
|---|---|---|---|
| Square Root | 2 | √ | √9 = 3 |
| Cube Root | 3 | ∛ | ∛8 = 2 |
| Fourth Root | 4 | ⁴√ | ⁴√16 = 2 |
| Fifth Root | 5 | ⁵√ | ⁵√32 = 2 |
| Sixth Root | 6 | ⁶√ | ⁶√64 = 2 |
- Algebra: Solve radical equations and simplify expressions with roots
- Geometry: Calculate dimensions and volumes from given areas or volumes
- Physics: Determine velocities, frequencies, and wave properties
- Engineering: Calculate scaling factors and dimensional analysis
- Finance: Compute compound interest rates and growth factors
Frequently Asked Questions
What is an nth root?
An nth root of a number is a value that, when raised to the power n, gives the original number. For example, the cube root of 8 is 2 because 2³ = 8.
How do you calculate nth roots?
Nth roots can be calculated using the formula ⁿ√x = x^(1/n). For perfect powers, the result is exact. For other numbers, approximation methods are used.
What are common roots?
Common roots include square root (n=2), cube root (n=3), fourth root (n=4), and fifth root (n=5). Square root and cube root are the most frequently used.