# Nth Root Calculator

Calculate nth roots with configurable degree, including odd roots of negative numbers

> Canonical page: https://elysiatools.com/en/tools/nth-root-calculator

- **Category:** Math & Numbers

- **Keywords:** nth root, calculator, math, radical

## Overview

The Nth Root Calculator is a precise mathematical utility designed to compute the nth root of any given number. It supports customizable root degrees up to 100, seamlessly handles odd roots of negative numbers, and allows you to specify the exact number of decimal places for your results. With built-in mathematical verification, it ensures accuracy for complex algebra, engineering, and physics calculations.

## Inputs

- **Radicand** (text): e.g. 81 or -32
- **Root Degree** (number)
- **Decimal Places** (number)
- **Show Verification** (checkbox)

## When to use

- When you need to calculate complex roots beyond standard square or cube roots for engineering or physics equations.
- When working with negative radicands that require an odd root degree, such as finding the 5th root of -32.
- When you need to verify mathematical computations by raising the calculated root back to its original power.

## How it works

- Enter the base number (radicand) you want to calculate the root for, such as 81 or -32.
- Specify the root degree (between 2 and 100) and choose your preferred number of decimal places.
- Enable the verification option if you want the tool to prove the result by raising it back to the specified degree.
- View the calculated nth root, exact integer status, and verification data in the structured JSON output.

## Use cases

- Solving advanced algebra and calculus problems that involve higher-degree radicals.
- Calculating geometric dimensions, such as finding the side length of a hypercube given its volume.
- Determining compound interest rates or financial growth factors over a specific number of periods.

## Frequently asked questions

### Can this calculator handle negative numbers?

Yes, it can calculate odd roots of negative numbers (e.g., the 3rd root of -27 is -3). Even roots of negative numbers are not supported as they result in imaginary numbers.

### What is the maximum root degree I can calculate?

You can set the root degree anywhere from 2 (a standard square root) up to 100.

### How accurate are the decimal results?

You can configure the precision up to 15 decimal places using the Decimal Places setting.

### What does the 'Show Verification' feature do?

It takes the calculated root and raises it back to the power of the root degree to prove the math matches your original radicand.

### What is a radicand?

The radicand is the number under the radical symbol—the base value you are trying to find the root of.

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