{
    "name": "Root Calculator",
    "url": "https://calculators.geekmidst.com/calculators/root-calculator",
    "markdown": "https://calculators.geekmidst.com/calculators/root-calculator.md",
    "category": "Mathematics",
    "description": "Calculate the square root, cube root or any nth root of a number, and see the simplified radical form such as √72 = 6√2.",
    "summary": "The nth root of x is the number that gives x when multiplied by itself n times. Negative numbers have real odd roots but no real even roots.",
    "also_called": [
        "Square root calculator",
        "Cube root calculator",
        "Radical calculator"
    ],
    "applies_to": "Worldwide",
    "last_updated": "2026-10-29",
    "computation": "Results are computed in the visitor’s browser on the HTML page. This API describes the calculator; it does not compute results.",
    "inputs": [
        {
            "name": "x",
            "label": "Number",
            "type": "number",
            "default": "72"
        },
        {
            "name": "n",
            "label": "Root index (n)",
            "type": "number",
            "default": "2"
        }
    ],
    "outputs": [
        {
            "key": "root",
            "label": "Root",
            "format": "text"
        },
        {
            "key": "simplified",
            "label": "Simplified radical",
            "format": "text"
        },
        {
            "key": "perfect",
            "label": "Exact whole-number root?",
            "format": "text"
        },
        {
            "key": "check",
            "label": "Check",
            "format": "text"
        }
    ],
    "formula": {
        "text": "ⁿ√x = x^(1/n);  simplify by taking out every prime factor that appears n times: √(k²·m) = k√m",
        "variables": {
            "x": "the radicand",
            "n": "the index of the root"
        }
    },
    "worked_example": {
        "inputs": {
            "x": "72",
            "n": "2"
        },
        "steps": [
            "72 = 2³ × 3² = (2 × 3)² × 2 = 36 × 2.",
            "√72 = √36 × √2 = 6√2.",
            "6 × 1.41421356 = 8.4852813742."
        ],
        "result": "The square root of 72 is 6√2, about 8.4853."
    },
    "interpretation": "The simplified radical is exact; the decimal is rounded to 10 places. A number with an exact whole-number root (64 for square and cube roots) is a perfect power.",
    "assumptions": [
        "Only real roots are returned: the principal (positive) root for even n."
    ],
    "limitations": [
        "Simplified radicals are shown for whole numbers only.",
        "Complex roots of negative numbers are not covered."
    ],
    "rules": null,
    "faqs": [
        {
            "question": "Why is there no square root of −4?",
            "answer": "No real number squared is negative. The answer is the imaginary number 2i, which this calculator does not cover."
        },
        {
            "question": "Does 25 have two square roots?",
            "answer": "Yes, 5 and −5. The √ symbol means the principal (non-negative) root, 5."
        }
    ],
    "sources": [],
    "related": [
        {
            "name": "Prime Factorization Calculator",
            "url": "https://calculators.geekmidst.com/calculators/prime-factorization-calculator"
        },
        {
            "name": "Pythagorean Theorem Calculator",
            "url": "https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator"
        },
        {
            "name": "Fraction Calculator",
            "url": "https://calculators.geekmidst.com/calculators/fraction-calculator"
        }
    ],
    "disclaimer": null,
    "publisher": "GM¹X CalcVerse"
}