# Radical Calculator

URL: https://speedycalculator.com/calculators/math/radical/
Last updated: 2026-10-30

> The radical calculator evaluates ⁿ√x for any degree n and simplifies it to the form a·ⁿ√b when x is a whole number, e.g. √72 = 6√2.

## Inputs

- Number (radicand)
- Radical degree n

## Results

- Simplified radical
- Decimal value

## Formula

```
ⁿ√x = x^(1/n),  ⁿ√(aⁿ·b) = a·ⁿ√b
```

## Explanation

Radicals are roots: square roots, cube roots and higher. In exact maths they are kept in simplified radical form rather than rounded, which makes later steps cleaner and answers exact.

### How to use the Radical Calculator

- **Number (radicand)**
- **Radical degree n**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

The decimal value uses x^(1/n). For whole numbers the calculator factorises x and moves every group of n identical prime factors outside the radical.

## Worked example

Inputs — Number (radicand): 72; Radical degree n: 2.

Results — **Simplified radical = 6√2**; Decimal value = 8.48528137424.

## Key terms

- **Radical**: An expression with a root sign.
- **Index**: The degree n of the root.

## FAQ

**What is the radicand?**
The number under the radical sign.

**How do I simplify √50?**
50 = 25 × 2, so √50 = 5√2.

**What is the index of a radical?**
The degree n in ⁿ√x; square roots have index 2.

**Can I take an even root of a negative number?**
Not in the real numbers.


## Sources

- [OpenStax – Intermediate Algebra 2e](https://openstax.org/details/books/intermediate-algebra-2e)
- [Wolfram MathWorld – Radical](https://mathworld.wolfram.com/Radical.html)