We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
We use cookies.This website uses essential cookies to operate core features. With your consent, we also use analytics cookies to understand traffic and improve the service. For more details, see our .
Was this tool helpful to use?
Your feedback helps us make it better
Calculate the nth root of any real number. Supports integer and decimal exponents, perfect for students and engineering professionals.
Enter details to see results
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
An nth root reverses raising a value to the nth power. In y = x1/n, x is the radicand (the value under the radical), n is the root index, and y is the displayed principal real root. Enter the index itself: for the cube root of 27, enter x = 27 and n = 3, giving 3 because 33 = 27. Entering 1/3 in the index box instead uses an exponent of 3.
For a negative radicand, the calculator returns a real value only when the index is an odd integer. For example, the real cube root of −8 is −2. An even root of a negative number is not real, and this calculator does not return complex values. For a positive radicand it returns one principal real value: the principal square root of 81 is 9, although the equation y2 = 81 has solutions 9 and −9.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Put the number under the root in x and the root order in n. For the cube root of 27, use x = 27 and n = 3.
Select from 0 through 10 decimal places. With rounding off, a non-integer result is truncated toward zero at the selected place; with rounding on, it is rounded for display.
Raise the displayed value to n and compare it with x. Exact examples such as 27 and 3 verify directly. A rounded decimal may differ slightly when raised back to its power.
Use cases
See how the tool fits into real work and everyday tasks.
When studying square, cube, or higher roots, enter the radicand and index separately, then check the inverse power relationship in the displayed equation.
For a positive measurement or an eligible negative value with an odd integer index, calculate a decimal result and record the chosen precision with your working notes.
Q&A
Find concise answers to common questions and confusing cases.
The calculation uses the reciprocal exponent 1/n, which is undefined when n is zero, so no result is produced.
No real number raised to an even integer power is negative. The calculator reports real roots only, so it does not provide a complex result.
The calculator displays the principal square root, which is nonnegative. When solving y² = x for positive x, include both signs in the equation’s solution.
No. The setting controls how the numeric result is displayed or truncated; it does not make the underlying floating-point calculation exact.
Notes
Review scope, result limitations, and important precautions before use.
Results are numeric real values formatted to the selected number of decimal places. This tool does not simplify symbolic radicals, calculate complex roots, or list every solution of an equation. For formal work, retain the expression and verify by raising the result to the entered index; use exact algebra when a rounded decimal is insufficient.
Related
Discover related tools, collections, and available API capabilities.