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:

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

Response:

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

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

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

HTTP (no key)

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.

CLI

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

Get the client at /clients/cli/.

Related tools

• Integer sqrt: Compute the exact floor of the square root of a non-negative integer string.
• Integer catalan number: Compute the nth Catalan number exactly.
• 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: Replace an array of canonical integer strings with consecutive first differences.
• Array integer clamp: Clamp an array of canonical integer strings to optional inclusive min and max bounds.
• Array integer cumulative sum: Replace an array of canonical integer strings with equal-length prefix sums.