SQRT

Compute the non-negative square root of a non-negative number.

Category: mathReturns: DOUBLEDialect: Standard

Syntax

SQRT(expr)

Description

## Overview Returns the non-negative principal square root of the input. SQRT is a foundational primitive for Euclidean distance, standard deviation (as SQRT of variance), root-mean-square error, and any quadratic-form calculation. Because real square roots are defined only for non-negative inputs, SQRT's domain is restricted. A negative input returns NULL rather than raising an error, so callers that depend on early detection of bad data should validate inputs explicitly or wrap the call in a CASE expression. ## Behavior - Domain: [0, infinity). Negative values return NULL. - Range: [0, infinity). - Returns NULL if the argument is NULL. - SQRT(0) is exactly 0. - SQRT of an exact perfect square (1, 4, 9, 16, ...) returns an exact integer in floating-point. - Integer inputs are implicitly cast to DOUBLE before the call. ## Numeric precision - Uses the IEEE 754 double-precision sqrt routine, correctly rounded to within 0.5 ULP (the strictest accuracy guarantee in the IEEE 754 standard). - For well-formed inputs, SQRT is one of the most numerically stable scalar functions available. - SQRT(POW(x, 2)) returns |x|, not x. ## Compatibility - Conforms to the SQL standard definition of SQRT as a scalar DOUBLE function with domain x >= 0. - Matches typical mathematical library implementations.

Parameters

Name	Type	Description
`expr`		Specifies the non-negative input whose square root is returned. Must be greater than or equal to 0. Negative values return NULL.

Examples

-- Basic literal
SELECT SQRT(4);
-- Result: 2.0

-- Irrational result
SELECT SQRT(2);
-- Result: 1.4142135623730951

-- SQRT of zero
SELECT SQRT(0);
-- Result: 0.0

-- Domain violation: negative input returns NULL
SELECT SQRT(-1);
-- Result: NULL

-- Identity: SQRT(x) equals POW(x, 0.5)
SELECT SQRT(9), POW(9, 0.5);
-- Result: 3.0, 3.0

-- Euclidean distance in 2D
SELECT SQRT(POWER(x2 - x1, 2) + POWER(y2 - y1, 2)) AS distance
FROM geometry.samples.segments;

Pitfalls

SQRT of a negative number returns NULL, not an error. Rows with negative variance (a sign of a bug) propagate silently as NULL through downstream aggregates.
Computing SQRT(POW(x, 2) + POW(y, 2)) can overflow or underflow intermediate values. Use HYPOT(x, y) for the numerically stable alternative.
SQRT(POW(x, 2)) equals |x|, not x. To recover x, keep sign information separately or use SIGN(x) * SQRT(POW(x, 2)).
Integer inputs are promoted to DOUBLE, which loses precision for BIGINT above 2^53. Cast to DECIMAL and then to DOUBLE only after the magnitude is manageable.