Nth Root Calculator
Calculate the nth root of any number, including square, cube and higher roots. Handles negative numbers with odd roots.
Last reviewed by the Radiatus Cloud team
Find the nth root of a number – the value that raised to the power n gives your number.
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Calculate any root of a number
The nth root of a number x is the value that, when raised to the power n, gives back x. The square root uses n equal to two, the cube root uses n equal to three, and higher roots use larger values. This calculator computes the nth root for any degree you enter, using the identity that the nth root of x equals x raised to the power one over n.
Negative numbers are handled carefully. A negative number has a real nth root only when n is an odd whole number, such as the cube root of minus eight being minus two. Even roots and non-integer roots of negative numbers are not real, and the tool says so rather than returning a misleading figure.
Roots in study and work
Roots appear across mathematics and science: geometry uses square and cube roots for lengths and volumes, statistics uses roots in standard deviation, and finance uses roots to find average growth rates over several periods. Engineers and students reach for nth roots whenever they need to reverse a power.
A verification line raises the result back to the power n so you can confirm it reproduces your original number, within normal floating-point precision. All calculation runs locally in your browser.
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Frequently Asked Questions
What is an nth root?
It is the number that, raised to the power n, equals your input. For example the fourth root of 81 is 3 because 3 to the fourth power is 81.
Can I take the root of a negative number?
Only for odd whole-number roots, such as the cube or fifth root. Even and fractional roots of negatives are not real numbers, and the tool reports that.
How do I get a square or cube root?
Enter a root degree of 2 for a square root or 3 for a cube root. Any degree works, including larger whole numbers and decimals.
Why does the verification differ slightly?
Computers store roots as floating-point approximations, so raising the result back to the power n may differ from the original in the final digits.
Can the degree be a decimal?
Yes for positive numbers. A decimal degree is treated as a fractional power, which is valid for non-negative inputs.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the number and the root degree n to compute the nth root.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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