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Nth Root Calculator

Math Calculators

Any-degree root of any number

Quick Answer

Nth Root Calculator: Any-degree root of any number. Nth Root Calculator uses standard math formulas to compute accurate results instantly.

3√27 =

3

Perfect power：3^3 = 27

Verify (root)ⁿ27
As exponentx^(1/3)
Squared9.00000
ln x / n1.0986

Steps

  1. 1ⁿ√x = x^(1/n) = e^(ln x ÷ n)
  2. 2ln 27 = 3.29584
  3. 3÷ 3 = 1.09861
  4. 4e^1.09861 = 3.00000000
  5. 5Check: 3^3 = 27 ✓ exact

Common perfect powers

RootValueWhy
∛822³ = 8
∛2733³ = 27
∜1622⁴ = 16
∜8133⁴ = 81
⁵√3222⁵ = 32
⁵√24333⁵ = 243
¹⁰√102422¹⁰ = 1024

💡 Even roots need x ≥ 0 (in reals); odd roots accept negatives: ∛(−8) = −2. Estimation: ⁿ√x ≈ x^(1/n) — for √, average a guess with x/guess and repeat (Newton). Geometric mean of n numbers is an nth root: GM = ⁿ√(x₁·x₂·…·xₙ).

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How to Use

  1. Enter values or expressions: type directly into the Nth Root Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Nth Root Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Any-degree root of any number.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Nth Root Calculator formula

Nth Root Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Nth Root Calculator?
Open the page and fill in the input fields — results update automatically. Any-degree root of any number.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Nth Root Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/nth-root

Results provided by this tool are for reference only and do not constitute professional advice.