Nth Root Calculator Formula

Understand the math behind the nth root calculator. Each variable explained with a worked example.

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Formulas Used

Result

result = pow(x, 1/n)

Verification

verification = pow(pow(x, 1/n), n)

Variables

VariableDescriptionDefault
xNumber27
nRoot (n)3

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)

    • Worked Example

    Find the cube root of 27.

    x = 27n = 3
    1. 01∛27 = 27^(1/3)
    2. 02= 3
    3. 03Verification: 3³ = 27

    Frequently Asked Questions

    What is an nth root?

    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.

    Learn More

    Guide

    How to Simplify Radicals - Complete Guide

    Learn how to simplify radical expressions step by step. Covers square roots, cube roots, rationalizing denominators, and operations with radicals.

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