In MongoDB, the $sqrt aggregation pipeline operator calculates the square root of a positive number and returns the result as a double.

$sqrt accepts any valid expression that resolves to a non-negative number.

Example

Suppose we have a collection called test with the following documents:

{ "_id" : 1, "data" : 100 }
{ "_id" : 2, "data" : 250 }

We can use the $sqrt operator to return the square root of the data field:

db.test.aggregate(
  [
    { $match: { _id: { $in: [ 1, 2 ] } } },
    { $project: { 
        squareRoot: { $sqrt: "$data" }
      }
    }
  ]
)

Result:

{ "_id" : 1, "squareRoot" : 10 }
{ "_id" : 2, "squareRoot" : 15.811388300841896 }

Negative Values

The $sqrt operator only accepts non-negative numbers.

Suppose we add the following document to our collection:

{ "_id" : 3, "data" : -100 }

Let’s apply the the $sqrt operator against that document:

db.test.aggregate(
  [
    { $match: { _id: { $in: [ 3 ] } } },
    { $project: { 
        squareRoot: { $sqrt: "$data" }
      }
    }
  ]
)

Result:

uncaught exception: Error: command failed: {
	"ok" : 0,
	"errmsg" : "$sqrt's argument must be greater than or equal to 0",
	"code" : 28714,
	"codeName" : "Location28714"
} : aggregate failed :
_getErrorWithCode@src/mongo/shell/utils.js:25:13
doassert@src/mongo/shell/assert.js:18:14
_assertCommandWorked@src/mongo/shell/assert.js:618:17
assert.commandWorked@src/mongo/shell/assert.js:708:16
DB.prototype._runAggregate@src/mongo/shell/db.js:266:5
DBCollection.prototype.aggregate@src/mongo/shell/collection.js:1046:12
@(shell):1:1

This error tells us that $sqrt’s argument must be greater than or equal to 0.

Null Values

Null values return null when using the $sqrt operator.

Suppose we add the following document to our collection:

{ "_id" : 4, "data" : null }

Let’s apply the the $sqrt operator against that document:

db.test.aggregate(
  [
    { $match: { _id: { $in: [ 4 ] } } },
    { $project: { 
        squareRoot: { $sqrt: "$data" }
      }
    }
  ]
)

Result:

{ "_id" : 4, "squareRoot" : null }

We can see that the result is null.

NaN Values

If the argument resolves to NaN, $sqrt returns NaN.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        squareRoot: { $sqrt: "$data" * 1 }
      }
    }
  ]
)

Result:

{ "_id" : 1, "squareRoot" : NaN }

Non-Existent Fields

If the $sqrt operator is applied against a field that doesn’t exist, null is returned.

Example:

db.test.aggregate(
  [
    { $match: { _id: 1 } },
    { $project: { 
        squareRoot: { $sqrt: "$age" }
      }
    }
  ]
)

Result:

{ "_id" : 1, "squareRoot" : null }