{
  "slug": "root",
  "title": "Root Calculator",
  "heading": "Root Calculator",
  "category": "math",
  "url": "https://www.revenuelab.fyi/toolbox/root",
  "summary": "Square root, cube root, and nth root of any number.",
  "description": "Handles any nth root, including odd roots of negative numbers, which are real even though a calculator that just uses Math.pow returns NaN.",
  "formula": "nth root of x = x^(1/n).",
  "dateModified": "2026-09-30",
  "run_url": "https://www.revenuelab.fyi/api/public/calc?tool=root",
  "inputs": [
    {
      "id": "value",
      "label": "Number",
      "kind": "number",
      "hint": null,
      "default": 729,
      "unit": null,
      "min": null,
      "max": null
    },
    {
      "id": "n",
      "label": "Root (n)",
      "kind": "number",
      "hint": null,
      "default": 3,
      "unit": null,
      "min": 1,
      "max": null
    }
  ],
  "outputs": [
    {
      "id": "nth",
      "label": "nth root",
      "format": "decimal",
      "hint": null,
      "primary": true
    },
    {
      "id": "note",
      "label": "Note",
      "format": "raw",
      "hint": null,
      "primary": false
    },
    {
      "id": "sqrt",
      "label": "Square root",
      "format": "decimal",
      "hint": null,
      "primary": false
    },
    {
      "id": "cbrt",
      "label": "Cube root",
      "format": "decimal",
      "hint": null,
      "primary": false
    }
  ],
  "worked_example": {
    "inputs": [
      "Number: 729",
      "Root (n): 3"
    ],
    "outputs": [
      "nth root: 9",
      "Note: Real root",
      "Square root: 27",
      "Cube root: 9"
    ]
  },
  "how_to": {
    "title": "How to use this",
    "steps": [
      "Enter number.",
      "Enter root (n).",
      "Read your nth root on the right — it updates as you type.",
      "Hit Share to keep the scenario or send it to someone."
    ]
  },
  "scenarios": [
    {
      "name": "Conservative",
      "description": "Lower-end numbers — what if things land soft?",
      "values": {
        "value": 437,
        "n": 2
      }
    },
    {
      "name": "Typical",
      "description": "Defaults — the most common real-world setup.",
      "values": {
        "value": 729,
        "n": 3
      }
    },
    {
      "name": "Ambitious",
      "description": "Higher-end numbers — what if things really pop?",
      "values": {
        "value": 1166,
        "n": 5
      }
    }
  ],
  "limitations": [
    "Results are rounded for display; the underlying calculation keeps full precision.",
    "Very large or very small inputs may hit floating-point limits in the browser.",
    "Inputs outside the accepted range are clamped rather than rejected."
  ],
  "faq": [
    {
      "q": "How does the root calculator work?",
      "a": "Handles any nth root, including odd roots of negative numbers, which are real even though a calculator that just uses Math.pow returns NaN. The underlying maths is: nth root of x = x^(1/n)."
    },
    {
      "q": "What do I need to enter?",
      "a": "2 values: number, and root (n). Each field starts with a sensible default, so you can change one number at a time and watch the result move."
    },
    {
      "q": "What does the nth root result mean?",
      "a": "It is returned as a decimal number and updates live as you edit the inputs, so you can compare two or three versions of a scenario in a few seconds."
    },
    {
      "q": "Is this calculator free, and do I need an account?",
      "a": "Yes, it's free, and no account is required. Nothing you type is stored on our servers — the maths runs entirely in your browser."
    },
    {
      "q": "How accurate is the result?",
      "a": "It applies the standard formula exactly, so the arithmetic is precise. Results are rounded for display; the underlying calculation keeps full precision."
    },
    {
      "q": "Who is this tool for?",
      "a": "It's built for students, developers, and anyone who needs the answer right now without setting up a spreadsheet."
    }
  ],
  "related": [
    "https://www.revenuelab.fyi/toolbox/exponent",
    "https://www.revenuelab.fyi/toolbox/logarithm"
  ],
  "license": "CC-BY-4.0",
  "citation": "RevenueLab — Root Calculator (https://www.revenuelab.fyi/toolbox/root)"
}