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Root Online Calculator

Reviewed by Calculator Editorial Team

Finding roots of numbers is a fundamental mathematical operation with applications in science, engineering, and everyday calculations. Our root online calculator makes it easy to compute square roots, cube roots, and nth roots with just a few clicks.

What is a Root Calculator?

A root calculator is an online tool that helps you find the roots of numbers. The most common roots are square roots (√) and cube roots (∛), but you can also calculate nth roots where n is any positive integer.

Roots are the inverse operation of raising a number to a power. For example, the square root of 16 is 4 because 4 × 4 = 16. Similarly, the cube root of 27 is 3 because 3 × 3 × 3 = 27.

Roots are used in many areas of mathematics and science, including algebra, geometry, physics, and engineering. They help solve equations, calculate distances, determine areas, and analyze data.

How to Use a Root Calculator

Using our root calculator is simple. Just follow these steps:

  1. Enter the number you want to find the root of in the "Number" field.
  2. Select the type of root you want to calculate (square root, cube root, or nth root).
  3. If you selected nth root, enter the value of n in the "Root" field.
  4. Click the "Calculate" button to get the result.
  5. Review the result and any additional information provided.

The calculator will display the root of the number you entered, along with a step-by-step explanation of how the calculation was performed.

Root Calculator Formula

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

x = y^(1/n)

Where:

  • x is the root of the number y
  • y is the number you want to find the root of
  • n is the root you want to calculate (2 for square root, 3 for cube root, etc.)

For example, to find the cube root of 27, you would use the formula:

x = 27^(1/3) = 3

This is because 3 × 3 × 3 = 27.

Root Calculator Examples

Here are some examples of how to use a root calculator:

Example 1: Square Root

Find the square root of 144.

  1. Enter 144 in the "Number" field.
  2. Select "Square root" from the "Root type" dropdown.
  3. Click "Calculate".

The calculator will display the result: √144 = 12.

Example 2: Cube Root

Find the cube root of 64.

  1. Enter 64 in the "Number" field.
  2. Select "Cube root" from the "Root type" dropdown.
  3. Click "Calculate".

The calculator will display the result: ∛64 = 4.

Example 3: Nth Root

Find the 5th root of 32.

  1. Enter 32 in the "Number" field.
  2. Select "Nth root" from the "Root type" dropdown.
  3. Enter 5 in the "Root" field.
  4. Click "Calculate".

The calculator will display the result: 32^(1/5) = 2.

Root Calculator FAQ

What is the difference between a square root and a cube root?
A square root is the value that, when multiplied by itself, gives the original number. A cube root is the value that, when multiplied by itself three times, gives the original number. For example, the square root of 16 is 4, while the cube root of 27 is 3.
Can I calculate the root of a negative number?
No, you cannot calculate the real root of a negative number using standard mathematical operations. However, you can calculate the root of a negative number using complex numbers, which are beyond the scope of this calculator.
What is the difference between a root and an exponent?
A root is the inverse operation of an exponent. For example, the square root of 16 is 4 because 4 × 4 = 16. Similarly, the cube root of 27 is 3 because 3 × 3 × 3 = 27. Exponents, on the other hand, represent repeated multiplication. For example, 4^2 = 16 and 3^3 = 27.