# Integer nth root

`integer-nth-root` · version 1.0.0 · Numbers & math · free, no key needed

Compute the exact floor of the nth root of a non-negative integer string.

**Use when you need to: integer nth root · nth root floor · integer root.**

## Supported

- integer nth root
- nth root floor
- integer root

## Not supported

- negative radicand
- even roots of negative numbers
- floating-point root

## Behavior

- value is a canonical non-negative integer string: 0 or a non-zero leading digit followed by digits, at most 1000 digits.
- degree is a JSON integer from 1 to 1000; degree 1 returns value unchanged.
- Negative values are rejected: only non-negative radicands are supported.
- The result is floor(value^(1/degree)), computed exactly by integer binary search (no floating point).
- is_exact is true exactly when result^degree equals value.

## Input

- `value` (string, required): max length 1000; pattern `^(0|[1-9][0-9]*)$`
- `degree` (integer, required): min 1; max 1000

## Output

- `result` (string, required)
- `is_exact` (boolean, required)

## Limits

- max digits: 1000
- min degree: 1
- max degree: 1000

## Example

Request input:

```json
{
  "value": "100",
  "degree": 3
}
```

Response:

```json
{
  "result": {
    "result": "4",
    "is_exact": false
  }
}
```

## How to call it

### MCP

Connect `https://computefirst.net/mcp` ([setup](/docs#connect)), then call `execute` with:

```json
{
  "id": "integer-nth-root",
  "version": "1.0.0",
  "input": {
    "value": "100",
    "degree": 3
  }
}
```

### HTTP (no key)

```sh
curl -X POST https://computefirst.net/v1/tools/integer-nth-root/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"value":"100","degree":3}'
```

The machine-readable contract is at [/v1/tools/integer-nth-root/versions/1.0.0](/v1/tools/integer-nth-root/versions/1.0.0).

### CLI

```sh
node cli.mjs run integer-nth-root 1.0.0 --input input.json --base-url https://computefirst.net
```

Get the client at [/clients/cli/](/clients/cli/).

## Related tools

- [Integer sqrt](/tools/integer-sqrt): Compute the exact floor of the square root of a non-negative integer string.
- [Integer catalan number](/tools/integer-catalan-number): Compute the nth Catalan number exactly.
- [Integer digital root](/tools/integer-digital-root): Repeatedly sum the base-b digits of the magnitude of an integer string until a single digit remains.
- [Array integer adjacent diff](/tools/array-integer-adjacent-diff): Replace an array of canonical integer strings with consecutive first differences.
- [Array integer clamp](/tools/array-integer-clamp): Clamp an array of canonical integer strings to optional inclusive min and max bounds.
- [Array integer cumulative sum](/tools/array-integer-cumulative-sum): Replace an array of canonical integer strings with equal-length prefix sums.