Nth root calculator
Enter the number and the root degree to get the real root and see whether the number is a perfect power.
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How to use it
- Enter number x and root degree n.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
The nth root of x is r with rⁿ = x, computed as r = x^(1/n). A negative x has a real root only for odd n: r = -(|x|^(1/n)).
Example
Inputs: Number x = 27, Root degree n = 3. Result: Root: 3; Check: root to the power n: 27; Perfect power?: Yes.
Limits and caveats
- Gives the real root only, not the complex roots.
- Non-exact roots are shown as rounded decimals.
Questions about this tool
Does a negative number have a cube root?
Yes, the cube root of -8 is -2 because (-2)³ = -8. Even roots of negative numbers are not real.
What is a perfect power?
A number whose root is a whole number, like 16, a perfect fourth power since 2⁴ = 16.
How do I get a square root?
Set the root degree n to 2.