The nth root of a number x is the value that, when multiplied by itself n times, equals x. For example, the 4th root of 16 is 2 because 2⁴ = 16.

How is nth root related to exponents?

Taking the nth root is the same as raising to the power 1/n. So ⁿ√x = x^(1/n).

Can you take the nth root of a negative number?

For odd values of n, yes. For example, ∛(-8) = -2. For even values of n, the nth root of a negative number is not a real number.

Nth Root Calculator

Calculate the nth root of any number. Find square roots, cube roots, or any nth root.

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Number

Root (n)

Result

3.00000000

Verification27.0000

View formula & how it works →

How to Calculate the Nth Root

Formula

ⁿ√x = x^(1/n)

The nth root of x is the number that, when raised to the nth power, gives x.

Common Roots

Square root (n=2): √x = x^(1/2)

Cube root (n=3): ∛x = x^(1/3)

Fourth root (n=4): ⁴√x = x^(1/4)

Example Calculation

Find the cube root of 27.

01∛27 = 27^(1/3)
02= 3
03Verification: 3³ = 27

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