Root Calculator

Calculate square roots, cube roots, and general nth roots with step-by-step verification and mathematical properties.

Calculate square roots, cube roots, and general nth roots with step-by-step verification.

Square Root Calculator

Result

4 = 2.000000

2² = 4

=2.000000

Cube Root Calculator

³√=?

General Root Calculator

=?

About Root Calculations

Root calculations find the number that, when raised to a specific power, equals the given number. The square root finds a number that, when squared, equals the input. The cube root finds a number that, when cubed, equals the input. General roots work for any positive integer power.

Key Properties:

  • • √x = x^(1/2)
  • • ³√x = x^(1/3)
  • • n√x = x^(1/n)
  • • √(a × b) = √a × √b
  • • √(a/b) = √a / √b
  • • (√a)² = a

Common Applications:

  • • Geometry and area calculations
  • • Physics and engineering
  • • Financial calculations
  • • Statistics and data analysis
  • • Computer graphics
  • • Scientific research

Important Notes:

  • • Square root of negative numbers is not a real number
  • • Even roots of negative numbers are not real numbers
  • • Odd roots of negative numbers are real numbers
  • • Root of zero is always zero