How this calculator works
An nth root reverses raising a number to the nth power. Odd degrees have one real root, including for negative radicands. Even degrees return the non-negative principal root. Solving for a degree uses logarithms and accepts only a matching positive integer from 1 to 1000.
Formula
r^n = x; r = x^(1/n); x = r^n. For non-zero magnitudes with |r| != 1, n = ln|x| / ln|r|, followed by a sign and integer check.
Worked example
The cube root of 27 is 3 because 3 × 3 × 3 = 27. The cube root of -125 is -5. If 2^n = 32, the degree is 5.
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Frequently asked questions
Why does a negative cube root exist?
Multiplying three negative factors gives a negative product, so an odd root can preserve a negative sign.
What does principal root mean?
For an even degree, two opposite real numbers can have the same power. The principal root is the non-negative one.
Can every pair determine a degree?
No. Zero and roots with magnitude 1 can be ambiguous, and other pairs may require a non-integer degree outside this tool.