MultiConvers

Root Calculator

Enter a number and the root degree (2 for square root, 3 for cube root, and so on) to get the principal real root.

How it works

The nth root of x is the number r such that r^n = x. Square root is degree 2; cube root is degree 3. Even roots of negative numbers are not real. Odd integer roots of negatives are: ³√−8 = −2. A 0th root is undefined.

The identity used is x^(1/n), with a sign correction for odd roots of negatives because ordinary floating-point power returns NaN there.

Formula

ⁿ√x = x^(1/n)
√9 = 3
³√−8 = −2

Worked examples

  • Square root

    9 with degree 2 → 3

  • Cube root of a negative

    −8 with degree 3 → −2

Useful notes

  • This returns the principal real root, not every complex root.
  • To raise a number to an arbitrary power, use the exponent calculator.

FAQ

How do I find a square root?

Use degree 2. The square root of 9 is 3 because 3×3 = 9.

Can I take an even root of a negative number?

Not on the real line. There is no real number whose square is −9. The tool reports no result instead of NaN.

Is the cube root of a negative allowed?

Yes. (−2)×(−2)×(−2) = −8, so ³√−8 = −2.

Related tools

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