Nth Root Calculator
Quickly calculate any root with our nth root calculator. Enter a number and the root value to instantly find accurate results for your mathematical needs.
What is an Nth Root?
The nth root of a number is a value that, when raised to the power of n, equals the original number. For example: 4th root of 16 = 2 because 2 × 2 × 2 × 2 = 16.
Nth Root Formula
Nth Root
Where:
Example:
5th root of 32 = 32^(1/5) = 2
Example Calculations
Nth Root Calculator
An nth root calculator finds the number that, when raised to the power of n, equals the given number.
Mathematically: If xⁿ = N, then x = ⁿ√N
Real-Life Example
Suppose you want to calculate the 4th root of 16:
- 4th root of 16 = 16^(1/4) = 2 because 2 × 2 × 2 × 2 = 16
- 3rd root (cube root) of 27 = 27^(1/3) = 3
- 5th root of 32 = 32^(1/5) = 2
Key Insight
Nth root calculations are useful in algebra, geometry, and physics. For example, if a 4-dimensional hypercube has a volume of 16 units⁴, the side length of the hypercube is 2 units, which is the 4th root of 16.
Why Use an Nth Root Calculator?
An Nth Root Calculator saves time and ensures accurate results, especially for large numbers, decimal values, and higher-order roots that are complex to solve manually.
Applications of Nth Roots
- Algebra and solving polynomial equations.
- Geometry for calculating dimensions from volume or area.
- Engineering and physics for modeling growth and decay.
- Finance for compound interest and investment calculations.
- Data science and statistics in normalization and scaling.