HOW TO use the nth root (any degree)?

Set degree n > 0. For even n, x must be ≥ 0; for odd n, x can be negative. The tool shows the computed value and key properties.

HOW TO improve precision?

Enter values with full precision. The calculator uses double-precision and switches to scientific notation for extreme magnitudes.

HOW TO reset the calculator?

Select Reset to clear inputs, messages, and results instantly.

HOW TO use the nth root (any degree)?

Set degree n > 0. For even n, x must be ≥ 0; for odd n, x can be negative. The tool shows the computed value and key properties.

HOW TO improve precision?

Enter values with full precision. The calculator uses double-precision and switches to scientific notation for extreme magnitudes.

HOW TO reset the calculator?

Select Reset to clear inputs, messages, and results instantly.

Root Calculator | TheCalculatorToolbox

Root Calculator | Square, Cube, nth Root Solver (Fast & Mobile-Friendly)

Enter values

Number x

x

For even n, x ≥ 0. For odd n, x can be negative.

Degree n

n

n > 0 (use decimals for fractional roots if needed)

Quick-set buttons help pick common root degrees fast.

Understand roots: square, cube, and nth

The nth root answers: “which number raised to the power n equals x?” Formally, n√x = x^{1/n}. Square roots (n = 2) return the principal non-negative root. Cube roots (n = 3) exist for all real x, including negatives. This calculator computes n√x with domain validation, shows key steps, and provides context values.

Domain rules and special cases

Even n: x must be ≥ 0 for real roots, principal root is non-negative.

Odd n: x can be negative; ∛(−8) = −2 is valid.

Exact hits: When the result is an integer (like √256 = 16), the tool highlights it.

Fractional n: You can use non-integer n to explore generalized root behavior (x^{1/n}).

Key properties

Power relation: n√x = x^{1/n}

Multiplicative: n√(ab) = n√a · n√b (when defined)

Scaling: n√(k^n · x) = k · n√x

Who benefits

Students: Algebra, geometry, and exam prep.

Engineers & scientists: Signal scales, materials, and growth models.

Analysts & finance: Normalization and compounding insights.

Designers: Proportional scaling using root-based transformations.

How to read the results

Root value: The computed n√x with precision and scientific notation when needed.

Power check: Shows (n√x)^n as a validation step (should equal x within rounding).

Context values: √x, ∛x, x^{1/4} for comparison, when appropriate.

Notes: Domain messages explain why some inputs are invalid for real roots.

FAQs

HOW TO calculate a square root?

Enter x and set n = 2, then select Calculate. For real results, x must be ≥ 0. The calculator returns the principal root.

HOW TO find a cube root?

Set n = 3 and enter any real x. Cube roots exist for negatives too, e.g., ∛(−27) = −3.

HOW TO use nth root for any degree?

Use n > 0. Even n requires x ≥ 0 for real roots; odd n allows negative x. The tool displays checks and context values.

HOW TO interpret precision and scientific notation?

Very small or large values appear in scientific notation. You can trust the double-precision outputs for typical math tasks.

HOW TO reset inputs?

Select Reset to clear x, n, messages, and results instantly.

HOW TO use this globally?

The calculator is country-neutral and client-side, using standard mathematical notation without regional settings.

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