Root Calculator
Calculate square roots, cube roots, and nth roots with step-by-step solutions and visualizations.
Calculator
Enter a number and select the root index to calculate the root value.
Result
0
Detailed Results
Step-by-Step Solution
Complete User Guide
What is a Root?
A root is the inverse operation of exponentiation. The nth root of a number x is a number y such that y^n = x.
- Square Root (√): The 2nd root (e.g., √16 = 4)
- Cube Root (∛): The 3rd root (e.g., ∛27 = 3)
- Nth Root: The nth root (e.g., 4th root of 16 = 2)
Perfect Roots
A perfect root is when the result is a whole number:
- Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100...
- Perfect cubes: 1, 8, 27, 64, 125, 216...
Examples
Example 1: Square Root
Input: Number = 16, Root Index = 2
Result: √16 = 4 (perfect square)
Example 2: Cube Root
Input: Number = 27, Root Index = 3
Result: ∛27 = 3 (perfect cube)
Example 3: Decimal Root
Input: Number = 10, Root Index = 2
Result: √10 ≈ 3.162278