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Nth Root Calculator

Find the nth root of any number.

How it is calculated

The n-th root of a value v is the number that, multiplied by itself n times, gives v. The tool computes it as v1/n. Degree 2 gives the square root and degree 3 the cube root; the degree may also be a decimal. A degree of 0 gives no result. For a negative value and an odd whole degree the tool returns the real negative root, so the cube root of −8 is −2. For a negative value and an even degree, or any fractional degree, there is no real answer and nothing is shown. Complex roots are not calculated. The result is rounded to two decimals.

Worked example

Find the cube root of 200. Use degree n = 3 and compute 2001/3. Since 5³ = 125 and 6³ = 216, the answer lies between 5 and 6, close to 6. The tool gives 5.85. Check: 5.85 × 5.85 × 5.85 is about 200.2, which agrees with 200 after rounding.

Try this example →

Common mistakes

  • Entering the root as 1/3 instead of 3 in the degree field. Degree 3 means the cube root.
  • Taking an even or fractional root of a negative number and expecting a result; real numbers have no such root.
  • Swapping value and degree, such as asking for the 200th root of 3.
  • Assuming the answer is exact. A root such as the cube root of 200 is irrational and shown rounded.
  • Forgetting that the n-th root of a number below 1 is larger than the number. The square root of 0.25 is 0.5.

About this calculator

This calculator finds the nth root of a number — the value that, when multiplied by itself n times, gives back the original number — covering not just the familiar square root (n=2) and cube root (n=3) but any degree of root, including fractional and negative inputs where applicable.

It's used in algebra and higher math whenever an equation involves fractional exponents or radicals beyond the square root, in engineering formulas that involve exponential growth or decay rates (solving for a periodic rate from a total growth factor often means taking an nth root), and by students checking root-based homework problems that a basic calculator's square-root key can't handle.

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Comments (1)

  • Editorial team

    A handy check is to raise the answer back to the power n and compare it with your starting value. The cube root of 27 should return 3, since 3 times 3 times 3 is 27. Stay with whole odd degrees for negative values: with an even or fractional degree, such as 1.5, the tool shows no result because there is no real root. Which roots do you need most, whole degrees or decimal ones?

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