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Nth Root Calculator

Calculate the Nth root of a number.

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Root Value

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Assumptions

  • The calculator returns the principal real root.
  • Even roots of negative numbers are not handled in the real number system.
  • The root value must be non-zero.

Sensitivity preview

Number -10%: Root Value 2.9

Number Current: Root Value 3

Number +10%: Root Value 3.1

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About this Root Calculator

Finding a root is the inverse operation of raising a number to an exponent. The most common is the Square Root (undoing a square), but this calculator can compute any 'Nth' root, such as a Cube Root or Fourth Root.

Who this calculator is for

  • Students solving radicals in algebra, geometry, or pre-calculus.
  • Anyone checking square roots, cube roots, or other nth roots by hand.
  • People reversing exponent problems or estimating precise decimal roots.

When to use it

  • Use this calculator when you need the square root, cube root, or any nth root of a number.
  • Use it to rewrite roots as fractional exponents and compare them to exponent problems.
  • Use it when a formula or measurement leaves you with a radical that needs a decimal approximation.

How to use this calculator

  1. Enter the Number (radicand).
  2. Enter the Root (n) you want to find (2 for Square Root, 3 for Cube Root).
  3. The result is the value that, when multiplied by itself 'n' times, equals your number.

Key assumptions

  • The calculator returns the principal real root.
  • Even roots of negative numbers are not handled in the real number system.
  • The root value must be non-zero.

Accuracy and testing

Review formula sources, default test cases, assumptions, unit handling, rounding rules, and changelog for this calculator.

View accuracy page

How this calculator works

The Nth root of x is written as $\sqrt[n]{x}$ or $x^{1/n}$. For example, $\sqrt[3]{8} = 2$ because $2 \times 2 \times 2 = 8$.

Inputs explained

Number

The value inside the radical symbol.

Root (n)

The degree of the root. Default is 3 (Cube Root). Set to 2 for Square Root.

Understanding your results

Most roots of integers are irrational numbers (decimals that go on forever). This calculator provides a precise decimal approximation.

Example scenarios

Square Root

Number 25, Root 2. Result = 5.

Cube Root

Number 27, Root 3. Result = 3.

Fifth Root

Number 32, Root 5. Result = 2.

Key Features

  • Supports any Nth root
  • Handles negative odd roots
  • High precision

Tips & Best Practices

  • You cannot take an even root (square, 4th, etc.) of a negative number in the real number system. It results in an imaginary number.
  • You CAN take an odd root (cube, 5th, etc.) of a negative number. The result is negative.

Glossary of Terms

Radicand
The number under the root symbol.
Index
The degree of the root (the 'n' in nth root).
Principal Root
The non-negative root of a number.

Frequently Asked Questions

How do I find a square root?
Set the 'Root (n)' field to 2.
Why can't I square root a negative number?
Because a negative number times a negative number is positive. There is no real number that, when squared, equals a negative. You need complex numbers (i) for that.
Is calculating the root the same as the power of 1/n?
Yes. Mathematically, $\sqrt[n]{x} = x^{1/n}$.