SQRT()

Syntax

How it works

SQRT() returns the non-negative square root of its argument. For an input x it returns the value r such that r * r = x. The result is always a floating point number, even when the input is a whole number and the root is exact, so SQRT(9) comes back as 3 stored as a DOUBLE.

It is mathematically the same as raising a number to the power of one half, so SQRT(x) is equivalent to POWER(x, 0.5). Most engines provide the dedicated SQRT() function because it reads more clearly and can be marginally faster than the general power routine.

SQRT() shows up constantly in distance and geometry work, most famously in the Euclidean distance formula SQRT(dx*dx + dy*dy), and in statistics, where the standard deviation is the square root of the variance. Pair it with ABS() when a value could be negative and you only care about its magnitude before taking a root.

Examples

Square root of a single value

SELECT SQRT(144) AS result;

result
------
    12

Euclidean distance between two points

-- straight line distance from (x1,y1) to (x2,y2)
SELECT SQRT(POWER(x2 - x1, 2) + POWER(y2 - y1, 2)) AS distance
FROM segments
WHERE id = 1;

distance
--------
       5

Square root of a column

SELECT id, area, SQRT(area) AS side_length
FROM squares
ORDER BY id;

id | area | side_length
---+------+------------
 1 |    4 |           2
 2 |   25 |           5
 3 |   90 |    9.486832

Relationship to POWER

-- SQRT(x) is the same as raising x to the power 0.5
SELECT SQRT(50)        AS with_sqrt,
       POWER(50, 0.5)  AS with_power;

with_sqrt | with_power
----------+-----------
 7.071068 |  7.071068

Distance from a fixed origin for every row

-- rank stores nearest to the (0,0) origin
SELECT name,
       SQRT(lat*lat + lng*lng) AS dist
FROM stores
ORDER BY dist ASC;

name    | dist
--------+---------
 Center |  0.5000
 North  |  3.2016
 East   | 12.8400

Common mistakes

-- Negative input: errors in SQL Server and PostgreSQL,
-- returns NULL in MySQL and SQLite
SELECT SQRT(-9);

-- Guard the input so a negative can never reach SQRT.
-- Use ABS() if you only want the magnitude, or a CASE
-- to return NULL deliberately.
SELECT CASE WHEN x >= 0 THEN SQRT(x) END AS root
FROM measurements;

-- Expecting an exact decimal, then comparing for equality
SELECT * FROM t
WHERE SQRT(area) = 9.486833;

-- SQRT returns a floating point value, so compare with a
-- tolerance instead of testing exact equality
SELECT * FROM t
WHERE ABS(SQRT(area) - 9.486833) < 0.00001;

Performance

SQRT() is a cheap scalar operation, but calling it inside a WHERE clause on an indexed column defeats the index, because the optimiser cannot use an index on col to satisfy a predicate on SQRT(col). Where possible, rewrite the comparison to keep the column bare, for example square both sides so SQRT(area) < 5 becomes area < 25.

For distance filtering, the same trick avoids the root entirely: to find rows within radius r, compare the squared distance dx*dx + dy*dy against r*r and skip SQRT() until you actually need the distance value for display. This is faster and, for a range test, mathematically identical.

Interview questions

SELECT SQRT(50) AS a, POWER(50, 0.5) AS b;

SELECT SQRT(POWER(x2 - x1, 2) + POWER(y2 - y1, 2)) AS distance
FROM segments;