Root Calculatorv1.0.0

Compute square roots, cube roots, and nth roots online with accurate rounding and clear formatting. Enter whole numbers, decimals, or simple fractions to test ideas quickly and compare values side by side. Use this root calculator to support math learning, geometry, statistics, engineering, and science with fast, consistent results.

Gain clarity by seeing principal real roots, readable thousands separators, and trimmed trailing zeros. Adjust decimal places to match assignment or publication standards and save your preferences for future sessions.

Calculate square roots, cube roots, and nth roots of real numbers with clear steps and precise rounding. Enter integers, decimals, or simple fractions to compare scenarios and verify work quickly.

• Enter a value in Enter a number (examples: 9, 2.25, 3/4, -8).
• Set Decimal places from 0 to 15 to control rounding.
• Check Include cube root to display ∛x.
• Check Include nth root to display n√x, then set Root degree (n ≥ 1).
• Click Calculate or type to trigger auto-calculation after a short pause.
• Click Clear to reset inputs, remove saved settings, and empty results.

• Square root: √x = x^(1/2). Real results require x ≥ 0.
• Cube root: ∛x = x^(1/3). Real results allow any real x, including negatives.
• nth root: n√x = x^(1/n). Even n requires x ≥ 0. Odd n allows any real x.
• Rational exponents: x^(m/n) = n√(x^m) when defined over the reals.
• Fractions: interpret a/b as a ÷ b when b ≠ 0.
• Rounding: round to the chosen decimal places and remove trailing zeros.
• Formatting: apply thousands separators to improve readability.

• Store inputs and preferences automatically with local storage.
• Interpret results as principal real roots unless specified otherwise.

Apply the Root Calculator to simplify algebra, size geometric shapes, analyze growth, and support engineering or science work. Check homework, validate hand calculations, and explore what-if scenarios with consistent rounding.

• Learn algebra: simplify expressions with √x, ∛x, and n√x; confirm steps that use rational exponents.
• Solve geometry: compute the side of a square from area (s = √A); estimate characteristic lengths from squared measures.
• Work with volume: find the edge of a cube from volume (a = ∛V); calculate a volumetric scale factor (scale = ∛(V₂/V₁)).
• Analyze growth: estimate compound growth or CAGR with nth roots (CAGR = (V₂/V₁)^(1/n) − 1).
• Do statistics: convert variance to standard deviation with a square root; check rounding and units.
• Support engineering and science: extract principal roots in formulas, compare scenarios, and document assumptions.

• Find a side length: if a square has area 81, compute √81 = 9 to get the side.
• Recover a cube edge: if a cube has volume 125, compute ∛125 = 5 to get the edge.
• Estimate growth: if an investment grows from 1000 to 1464.1 over 4 years, compute (1464.1/1000)^(1/4) − 1 ≈ 0.10 for 10 percent annual growth.
• Convert variance to standard deviation: if variance is 2.89, compute √2.89 = 1.7 for the standard deviation.

Enter whole numbers, decimals, or simple fractions like 3/4. The tool sanitizes input and handles commas. Fractions require a nonzero denominator.

Even roots of negative numbers have no real result. The calculator reports an error in those cases. Odd roots allow negative inputs.

Set decimal places from 0 to 15. The tool rounds to that precision, removes trailing zeros, and adds thousands separators for readability.