Nth Root Calculator Formula

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

Use the Nth Root Calculator

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

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    Open Nth Root Calculator