Root Calculator

Use this free online root calculator to find the square root, cube root, or any nth root of a number. Get step-by-step solutions and explanations.

Root Calculator

Enter a number and the root index (2 for square root, 3 for cube root, etc.), then click Calculate to find the result with step-by-step solution.

Result

What is a Root?

In mathematics, a root of a number x is another number, which when raised to a given power n, equals x. In other words, the nth root of x is a number r such that r^n = x.

For example, the square root (2nd root) of 9 is 3, because 3^2 = 9. The cube root (3rd root) of 8 is 2, because 2^3 = 8.

Types of Roots

  • Square Root (2nd Root): The square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the radical symbol √.
  • Cube Root (3rd Root): The cube root of a number is a value that, when multiplied by itself three times, gives the original number. It is denoted by the symbol ∛.
  • Fourth Root: The fourth root of a number is a value that, when raised to the power of 4, gives the original number. It is denoted by ∜.
  • nth Root: The nth root of a number is a value that, when raised to the power of n, gives the original number. It is denoted by the radical symbol with a small n: ⁿ√.

Root Calculation Formula

The formula for calculating the nth root of a number x is:

ⁿ√x = x^(1/n)

Where n is the root index (2 for square root, 3 for cube root, etc.) and x is the number for which we want to find the root.

How to Use the Root Calculator

  1. Enter the number for which you want to find the root.
  2. Enter the root index (2 for square root, 3 for cube root, etc.).
  3. Click 'Calculate' to find the root.
  4. View the result and step-by-step solution.

Applications of Roots in Real Life

  • Engineering and construction for calculating dimensions and structural stability.
  • Physics for determining relationships between variables in equations.
  • Finance for calculating compound interest and investment growth.
  • Computer graphics for scaling and transforming objects in 3D space.