What is the nth root of a number?

The nth root of a number x is a value r such that r raised to the power n equals x. For example, the cube root (n=3) of 27 is 3 because 3³ = 27.

Can I calculate the nth root of a negative number?

Yes — for odd roots (n=3, 5, 7, …) the result is a negative real number. For example, the cube root of −8 is −2. Even roots of negative numbers are complex; this tool will display a friendly error in that case.

How precise is the result?

Results are computed using JavaScript's native floating-point Math.pow and are accurate to at least 10 significant figures, which is sufficient for almost all practical purposes.

What is the difference between the square root and the nth root?

The square root is just the nth root where n=2. The nth root generalizes this to any degree: n=3 is the cube root, n=4 is the fourth root, and so on.

How do I express an nth root as an exponent?

The nth root of x equals x raised to the power 1/n. For example, the 5th root of 32 = 32^(1/5) = 2.

Nth Root Calculator

Name: Nth Root Calculator
Availability: InStock
Author: Nham Vu

Enter a number and a root degree to instantly compute the nth root with step-by-step working.

Enter Values

Radicand (the number)

Root Degree (n)

2 = square root · 3 = cube root · any positive integer

Quick Select

Result

Enter values and click Calculate

Copied!

Summary

Enter a number and a root degree to instantly compute the nth root with step-by-step working.

How it works

Enter the number (radicand) you want to find the root of.
Enter the root degree n (e.g. 2 for square root, 3 for cube root).
Click Calculate or press Enter.
The result displays in both radical form and as a decimal.
Step-by-step working shows the equivalent exponent calculation.
Use the swap button to reuse the result as a new input.

Use cases

Find the square root or cube root of any number quickly.
Solve radical equations in algebra homework.
Compute compound annual growth rate (CAGR) using the nth root.
Verify calculator results for math exams or standardized tests.
Explore irrational numbers and their decimal approximations.
Compute roots used in physics or engineering formulas.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu