Root Calculator
This skill performs mathematical root calculations including square roots, cube roots, and nth roots of numbers.
When to Use This Skill
Activate this skill automatically when the user:
- Asks to calculate a square root (e.g., "square root of 16", "sqrt(25)")
- Asks to calculate a cube root (e.g., "cube root of 27")
- Asks to calculate an nth root (e.g., "4th root of 81", "5th root of 32")
- Uses math keywords like "sqrt", "root of", "calculate root"
How to Use
When the user requests a root calculation:
Parse the request to identify:
- The number to calculate the root of
- The root type (square, cube, or nth root)
Perform the calculation using Python:
For square root:
import math
result = math.sqrt(number)
For cube root:
result = number ** (1/3)
For nth root:
result = number ** (1/n)
Handle edge cases:
- Negative numbers with even roots: Explain that the result is a complex number
- For negative numbers with odd roots: Use
abs(number) ** (1/n) * (-1 if number < 0 else 1)
- Very large or very small numbers: Use scientific notation if needed
Present the result clearly:
- Show the calculation performed
- Display the result with appropriate precision (typically 4-6 decimal places)
- For perfect roots, show the exact integer result
Examples
Example 1: Square Root
User: "What's the square root of 144?"
Claude: The square root of 144 is 12.
Example 2: Cube Root
User: "Calculate the cube root of 27"
Claude: The cube root of 27 is 3.
Example 3: Nth Root
User: "What's the 4th root of 81?"
Claude: The 4th root of 81 is 3.
Example 4: Non-Perfect Root
User: "Square root of 50"
Claude: The square root of 50 is approximately 7.0711.
Example 5: Negative Number (Odd Root)
User: "Cube root of -8"
Claude: The cube root of -8 is -2.
Example 6: Negative Number (Even Root)
User: "Square root of -16"
Claude: The square root of -16 is not a real number. In the complex number system, it equals 4i.
Error Handling
- Invalid input: If the user's request is unclear, ask for clarification
- Negative numbers with even roots: Explain that the result is complex (not a real number)
- Division by zero: If n=0 in nth root, explain this is undefined
- Very large results: Use scientific notation for readability
Notes
- Use Python's
math module for square roots for better precision
- For other roots, use the exponentiation operator
**
- Round results appropriately (typically 4-6 decimal places for non-perfect roots)
- Always show the exact integer if the result is a perfect root
