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Free online Nth root calculator

The nth root of a number x is the value r such that rⁿ = x. This calculator handles any integer root from 2 to 100, including negative values with odd degrees.

About this calculator

How to use

  1. Enter the number whose root you want to find.
  2. Set the degree (2 = square root, 3 = cube root, etc., up to 100).
  3. The result and step-by-step working appear instantly.
  4. Click “Share with my numbers” to copy a URL with your inputs.

Formula

ⁿ√x = x^(1/n)

For negative x with odd n:

ⁿ√(−|x|) = −(|x|^(1/n))

Root symbols

DegreeSymbol
2√ (square root)
3∛ (cube root)
4∜ (fourth root)
n ≥ 5ⁿ√

Worked examples

  • ∛64 = 4 (because 4³ = 64) — perfect root
  • ∜16 = 2 (because 2⁴ = 16) — perfect root
  • √2 ≈ 1.4142135624 — not a perfect root
  • ∛(−8) = −2 (real, odd root of negative number)
  • ⁴√(−16) — no real result (even root of negative)

Notes

  • Root degree must be an integer between 2 and 100.
  • Even roots of negative numbers have no real solution.
  • Results that are not perfect roots are shown to 10 significant figures.

References

  • Nth rootWikipedia · en.wikipedia.org
  • nth RootWolfram MathWorld · mathworld.wolfram.com

Frequently asked

What is the nth root?
The nth root of x is the number r such that rⁿ = x. The square root is the 2nd root, the cube root is the 3rd root, and so on.
Can I take an even root of a negative number?
No — an even root of a negative number produces a complex (imaginary) result, which this calculator does not support. Odd roots of negative numbers are real and are supported.
What is a perfect root?
A perfect root is one where the result is an exact integer. For example, ∛64 = 4 is a perfect cube root.
How is the nth root calculated?
The nth root of x is computed as x^(1/n). For negative x with odd n, the result is −(|x|^(1/n)).
What is the cube root of a negative number?
For any real odd root of a negative number, the result is negative. For example, ∛(−8) = −2 because (−2)³ = −8.

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