# Cube Root Calculator

Calculate the cube root or any nth root of a number. Verify results, check for perfect roots, and handle negative numbers. Free online root calculator.

## What this calculates

Calculate the cube root or any nth root of a number with this free online tool. Handles positive and negative numbers, verifies results, and identifies perfect roots.

## Inputs

- **Number** — The number to find the root of. Can be negative for odd roots.
- **Root Degree (n)** — min 2, max 100 — The degree of the root. 3 for cube root, 4 for fourth root, etc.

## Outputs

- **Result** — The nth root of the number.
- **Verification (result^n)** — The result raised to the nth power. Should equal the original number.
- **Perfect Root?** — formatted as text — Whether the result is an exact integer.

## Details

The nth root of a number x is a value r such that r^n = x. The cube root (n=3) is the most common after the square root. For example, the cube root of 27 is 3 because 3^3 = 27, and the cube root of -8 is -2 because (-2)^3 = -8.

Unlike square roots, cube roots are defined for negative numbers because a negative number raised to an odd power remains negative. Even roots (square root, fourth root, etc.) of negative numbers are not real numbers. This calculator handles both cases correctly.

Perfect roots are numbers whose nth root is an exact integer. For cube roots, the first several perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1000. Recognizing perfect cubes helps simplify radical expressions in algebra and makes mental math easier.

## Frequently Asked Questions

**Q: What is a cube root?**

A: A cube root of a number x is a value r such that r^3 = x. For example, the cube root of 64 is 4 because 4 x 4 x 4 = 64. The cube root symbol is a radical sign with a small 3. Every real number has exactly one real cube root.

**Q: Can you take the cube root of a negative number?**

A: Yes. Unlike square roots, cube roots of negative numbers are real. The cube root of -27 is -3 because (-3)^3 = -27. This works because multiplying a negative number an odd number of times produces a negative result.

**Q: What is the difference between a square root and a cube root?**

A: A square root finds r such that r^2 = x (the inverse of squaring). A cube root finds r such that r^3 = x (the inverse of cubing). Square roots of negative numbers are not real, while cube roots of negative numbers are real. The square root of 9 is 3, and the cube root of 27 is 3.

**Q: What are perfect cubes?**

A: Perfect cubes are integers that are the cube of another integer. The first 10 perfect cubes are: 1 (1^3), 8 (2^3), 27 (3^3), 64 (4^3), 125 (5^3), 216 (6^3), 343 (7^3), 512 (8^3), 729 (9^3), and 1000 (10^3).

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Source: https://vastcalc.com/calculators/math/cube-root
Category: Math
Last updated: 2026-04-21