Square Root Calculator
Calculate square roots, cube roots, and nth roots of numbers
Quick Examples
Root Operation Rules
Square Root:√a × √a = a (a ≥ 0)
Cube Root:∛a × ∛a × ∛a = a
nth Root:ⁿ√a = a^(1/n)
Operation Rules:√(ab) = √a × √b√(a/b) = √a / √b
Common Square Roots
√1:1
√4:2
√9:3
√16:4
√25:5
√36:6
√49:7
√64:8
√81:9
√100:10
√121:11
√144:12
Usage Instructions
• Enter the radicand to perform root calculations
• Supports square roots, cube roots, and arbitrary nth roots
• Displays exact and approximate values
• Automatically identifies perfect squares/cubes
• Provides calculation verification
• Negative numbers can only calculate odd roots
Mathematical Knowledge
• Square Root: If x² = a, then x is the square root of a
• Cube Root: If x³ = a, then x is the cube root of a
• Principal Root: The positive square root of a positive number is called the principal root
• Irrational Numbers: Square roots of non-perfect squares are irrational numbers
• Imaginary Numbers: Square roots of negative numbers do not exist in the real number system