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Home/Formula Library/Nth root

Nth root

Find b such that b raised to n equals a.

General

  • Percentage proportion
  • Percent error
  • Ratio and proportion
  • Rounding
  • Exponentiation
  • Nth root
  • Fraction arithmetic
  • Long division
  • Order of operations (PEMDAS)

Formula

ⁿ√a = b ⇔ bⁿ = a

Explanation

The principal nth root is the non-negative root when n is even and a ≥ 0. Even roots of negatives are not real. Odd roots allow negative radicands. Verify by raising the root back to n.

Variables

  • aradicand
  • nroot index (2 = square root, 3 = cube root, …)
  • bthe root

When to use

Geometry (side from area/volume), RMS-style calculations, and undoing powers.

Use this formula

Calculators

  • Root Calculator→

Related formulas

  • Exponentiationbase^exponent = result
  • Fraction arithmetica/b ± × ÷ c/d → reduced form

Other categories

  • Statistics
  • Cooking & apparel
  • Data & digital
  • Electricity & magnetism
  • Encodings & numbers
  • Date & time
Formula Library→

Popular

  • Percentage proportion
  • Arithmetic and weighted mean
  • Exponentiation
  • Fraction arithmetic
Formula Library→