Online Calculator with Nth Root Key
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Reviewed by Calculator Editorial Team
This online calculator with nth root key provides an easy way to calculate roots of any order. Whether you need to find the cube root, fourth root, or any other root, this tool will give you precise results quickly.
What is the Nth Root?
The nth root of a number is a value that, when raised to the power of n, gives the original number. For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.
In mathematical terms, if y is the nth root of x, then:
y = x^(1/n)
This concept is fundamental in algebra and has applications in various fields including engineering, physics, and finance.
How to Use the Calculator
Using the calculator is simple:
- Enter the number you want to find the root of in the "Number" field
- Select the root order (n) from the dropdown menu
- Click the "Calculate" button
- View your result in the result panel
The calculator will display the nth root of your number with up to 6 decimal places for precision.
Nth Root Formula
The formula for calculating the nth root of a number x is:
y = x^(1/n)
Where:
- y = the nth root of x
- x = the number you want to find the root of
- n = the root order (must be a positive integer)
This formula is implemented in the calculator's JavaScript to provide accurate results.
Worked Examples
Example 1: Square Root
Find the square root of 16.
y = 16^(1/2) = 4
The square root of 16 is 4 because 4 × 4 = 16.
Example 2: Cube Root
Find the cube root of 64.
y = 64^(1/3) = 4
The cube root of 64 is 4 because 4 × 4 × 4 = 64.
Example 3: Fourth Root
Find the fourth root of 81.
y = 81^(1/4) ≈ 3.000000
The fourth root of 81 is approximately 3 because 3 × 3 × 3 × 3 = 81.
Frequently Asked Questions
What is the difference between a square root and a cube root?
A square root is the value that, when multiplied by itself, gives the original number (n=2). A cube root is the value that, when multiplied by itself three times, gives the original number (n=3).
Can I calculate roots of negative numbers?
Yes, but the results will be complex numbers for odd roots and real numbers for even roots. The calculator handles both cases.
What happens if I enter a non-integer for the root order?
The calculator only accepts positive integers for the root order. Non-integer values will be rounded to the nearest integer.