> ## Documentation Index
> Fetch the complete documentation index at: https://axiom.co/docs/llms.txt
> Use this file to discover all available pages before exploring further.

<AgentInstructions>

## Submitting Feedback

If you encounter incorrect, outdated, or confusing documentation on this page, submit feedback:

POST https://axiom.co/docs/feedback

```json
{
  "path": "/apl/scalar-functions/mathematical-functions/sqrt",
  "feedback": "Description of the issue"
}
```

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</AgentInstructions>

# sqrt

> This page explains how to use the sqrt function in APL.

Use the `sqrt` function in APL to compute the square root of a non-negative numeric value.

`sqrt` is useful whenever you want to compress large numeric ranges, compute root-mean-square values, normalize metrics, or undo a squared transformation. It's equivalent to `pow(x, 0.5)` but is more concise for the square-root case.

If the input is negative, `sqrt` returns NaN (Not a Number). APL represents NaN as `null` in query results. Use [isnan](/apl/scalar-functions/mathematical-functions/isnan) to filter these values before aggregating or charting.

## For users of other query languages

If you come from other query languages, this section explains how to adjust your existing queries to achieve the same results in APL.

<AccordionGroup>
  <Accordion title="Splunk SPL users">
    In Splunk SPL, `sqrt()` works identically: it takes a single numeric argument and returns its square root.

    <CodeGroup>
      ```sql Splunk example theme={null}
      | eval root_duration = sqrt(req_duration_ms)
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend root_duration = sqrt(req_duration_ms)
      ```
    </CodeGroup>
  </Accordion>

  <Accordion title="ANSI SQL users">
    In ANSI SQL, `SQRT()` is a standard built-in function with the same semantics as in APL.

    <CodeGroup>
      ```sql SQL example theme={null}
      SELECT SQRT(req_duration_ms) AS root_duration FROM logs
      ```

      ```kusto APL equivalent theme={null}
      ['sample-http-logs']
      | extend root_duration = sqrt(req_duration_ms)
      ```
    </CodeGroup>
  </Accordion>
</AccordionGroup>

## Usage

### Syntax

```kusto theme={null}
sqrt(x)
```

### Parameters

| Name | Type | Required | Description                                                                         |
| ---- | ---- | -------- | ----------------------------------------------------------------------------------- |
| `x`  | real | Yes      | The value to compute the square root of. Must be non-negative for a defined result. |

### Returns

Returns the square root of `x`.

If `x` is negative, the function returns NaN, which APL represents as `null` in query results. Use [isnan](/apl/scalar-functions/mathematical-functions/isnan) to check for this condition.

## Examples

### Compute the square root of request duration

Use `sqrt` to normalize request durations by taking their square root, compressing the range of large values.

**Query**

```kusto theme={null}
['sample-http-logs']
| extend root_duration = sqrt(req_duration_ms)
| project _time, id, req_duration_ms, root_duration
| order by root_duration desc
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%20%7C%20extend%20root_duration%20%3D%20sqrt\(req_duration_ms\)%20%7C%20project%20_time%2C%20id%2C%20req_duration_ms%2C%20root_duration%20%7C%20order%20by%20root_duration%20desc%22%7D)

**Output**

| \_time              | id     | req\_duration\_ms | root\_duration |
| ------------------- | ------ | ----------------- | -------------- |
| 2024-11-14 10:00:00 | user-1 | 1600.0            | 40.0           |
| 2024-11-14 10:01:00 | user-2 | 400.0             | 20.0           |
| 2024-11-14 10:02:00 | user-3 | 25.0              | 5.0            |

### Detect NaN from negative inputs

When input values are negative, `sqrt` returns NaN. APL displays NaN as `null`. Use `isnan` to identify and handle these rows.

**Query**

```kusto theme={null}
['sample-http-logs']
| extend shifted = req_duration_ms - 500
| extend root_shifted = sqrt(shifted)
| extend is_invalid = isnan(root_shifted)
| project _time, id, shifted, root_shifted, is_invalid
```

[Run in Playground](https://play.axiom.co/axiom-play-qf1k/query?initForm=%7B%22apl%22%3A%22%5B'sample-http-logs'%5D%20%7C%20extend%20shifted%20%3D%20req_duration_ms%20-%20500%20%7C%20extend%20root_shifted%20%3D%20sqrt\(shifted\)%20%7C%20extend%20is_invalid%20%3D%20isnan\(root_shifted\)%20%7C%20project%20_time%2C%20id%2C%20shifted%2C%20root_shifted%2C%20is_invalid%22%7D)

**Output**

| \_time              | id     | shifted | root\_shifted | is\_invalid |
| ------------------- | ------ | ------- | ------------- | ----------- |
| 2024-11-14 10:00:00 | user-1 | 700.0   | 26.46         | false       |
| 2024-11-14 10:01:00 | user-2 | -200.0  | null          | true        |
| 2024-11-14 10:03:00 | user-3 | -50.0   | null          | true        |

## List of related functions

* [pow](/apl/scalar-functions/mathematical-functions/pow): Raises a value to an arbitrary power. `sqrt(x)` is equivalent to `pow(x, 0.5)`.
* [isnan](/apl/scalar-functions/mathematical-functions/isnan): Returns `true` when a value is NaN. Use it to detect `null` results from `sqrt` on negative inputs.
* [abs](/apl/scalar-functions/mathematical-functions/abs): Returns the absolute value. Use it to ensure inputs are non-negative before passing them to `sqrt`.
* [exp](/apl/scalar-functions/mathematical-functions/exp): Returns e^x. Use it when the inverse operation of `log` is needed rather than a root.
* [log](/apl/scalar-functions/mathematical-functions/log): Returns the natural logarithm. Use it alongside `sqrt` when working in log space.