Mathematics Roots Calculator

Find square roots, cube roots, and nth roots with our precise online calculator. This tool helps you solve mathematical root problems quickly and accurately.

What is a root?

In mathematics, a root of a number is a value that, when raised to a power, gives the original number. The most common roots are square roots and cube roots, but any positive integer can be used as the root.

Square root formula: √x = y where y² = x

Cube root formula: ∛x = y where y³ = x

Nth root formula: x^(1/n) = y where yⁿ = x

Roots are used in many mathematical applications, including solving equations, geometry, and physics. Understanding roots helps in various real-world problems like calculating areas, volumes, and distances.

How to use this calculator

Enter the number you want to find the root of in the "Number" field.
Select the type of root you want to calculate (square, cube, or nth root).
For nth root, enter the value of n in the additional field that appears.
Click the "Calculate" button to see the result.
Use the "Reset" button to clear all fields and start over.

Note: For negative numbers, only odd roots are defined in real numbers. Even roots of negative numbers result in complex numbers, which this calculator does not handle.

Formula used

The calculator uses the following mathematical formulas:

Square root: √x = x^(1/2)

Cube root: ∛x = x^(1/3)

Nth root: x^(1/n)

The calculator implements these formulas using JavaScript's built-in Math.pow() function for accurate results.

Worked examples

Here are some examples of how to use the calculator and interpret the results:

Example 1: Square root of 16

Enter 16 in the "Number" field.
Select "Square root" from the dropdown.
Click "Calculate".
The result will be 4, because 4 × 4 = 16.

Example 2: Cube root of 27

Enter 27 in the "Number" field.
Select "Cube root" from the dropdown.
Click "Calculate".
The result will be 3, because 3 × 3 × 3 = 27.

Example 3: 4th root of 16

Enter 16 in the "Number" field.
Select "Nth root" from the dropdown.
Enter 4 in the "n" field.
Click "Calculate".
The result will be 2, because 2 × 2 × 2 × 2 = 16.

Number	Root Type	Result
25	Square root	5
64	Cube root	4
81	4th root	3
1000	Cube root	10

Frequently Asked Questions

What is the difference between a square root and a cube root?: A square root of a number x is a number y such that y² = x. A cube root of a number x is a number y such that y³ = x. Square roots are the solutions to quadratic equations, while cube roots are solutions to cubic equations.
Can I find roots of negative numbers?: Yes, but only for odd roots. Even roots of negative numbers result in complex numbers, which this calculator does not handle. For example, the cube root of -8 is -2, but the square root of -4 is not a real number.
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 9 is 3 because 3² = 9. An exponent is the operation that raises a number to a power, while a root finds the number that, when raised to a power, gives the original number.
How accurate are the results from this calculator?: The calculator uses JavaScript's built-in Math.pow() function, which provides accurate results for most practical purposes. However, for very large or very small numbers, floating-point precision limitations may affect the results.
Can I use this calculator for scientific calculations?: Yes, this calculator is suitable for basic mathematical root calculations. For more advanced scientific calculations, you may need specialized software or programming tools.