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:

1. Parse the request to identify:

   • The number to calculate the root of
   • The root type (square, cube, or nth root)

2. 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)
   

3. 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

4. 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