# Root Calculator

> Calculate the square root, cube root or any nth root of a number, and see the simplified radical form such as √72 = 6√2.

Category: Mathematics · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/root-calculator

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.

## Inputs
- Number (default 72)
- Root index (n) (default 2)

## Results
- Root
- Simplified radical
- Exact whole-number root?
- Check

## Formula

```
ⁿ√x = x^(1/n);  simplify by taking out every prime factor that appears n times: √(k²·m) = k√m
```

Where:
- x: the radicand
- n: the index of the root

## Worked example
1. 72 = 2³ × 3² = (2 × 3)² × 2 = 36 × 2.
2. √72 = √36 × √2 = 6√2.
3. 6 × 1.41421356 = 8.4852813742.

**Result:** The square root of 72 is 6√2, about 8.4853.

## What the result means

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 and limits
- Only real roots are returned: the principal (positive) root for even n.
- Simplified radicals are shown for whole numbers only.
- Complex roots of negative numbers are not covered.

## Questions

### Why is there no square root of −4?

No real number squared is negative. The answer is the imaginary number 2i, which this calculator does not cover.

### Does 25 have two square roots?

Yes, 5 and −5. The √ symbol means the principal (non-negative) root, 5.

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Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/root-calculator