# sqrt, sqrtf, sqrtl

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< c‎ | numeric‎ | math

Defined in header `<math.h>` |  |
float sqrtf( float arg ); | (1) | (since C99)
double sqrt( double arg ); | (2) |
long double sqrtl( long double arg ); | (3) | (since C99)
Defined in header `<tgmath.h>` |  |
#define sqrt( arg ) | (4) | (since C99)

1-3) Computes square root of `arg`.
4) Type-generic macro: If `arg` has type long double, `sqrtl` is called. Otherwise, if `arg` has integer type or the type double, `sqrt` is called. Otherwise, `sqrtf` is called. If `arg` is complex or imaginary, then the macro invokes the corresponding complex function (csqrtf, csqrt, csqrtl).

### Parameters

arg | - | floating point value

### Return value

If no errors occur, square root of `arg` (\({\small \sqrt{arg} }\)√arg), is returned.

If a domain error occurs, an implementation-defined value is returned (NaN where supported).

If a range error occurs due to underflow, the correct result (after rounding) is returned.

### Error handling

Errors are reported as specified in `math_errhandling`.

Domain error occurs if `arg` is less than zero.

If the implementation supports IEEE floating-point arithmetic (IEC 60559),

- If the argument is less than -0, FE_INVALID is raised and NaN is returned.
- If the argument is +∞ or ±0, it is returned, unmodified.
- If the argument is NaN, NaN is returned

### Notes

`sqrt` is required by the IEEE standard to be correctly rounded from the infinitely precise result. In particular, the exact result is produced if it can be represented in the floating-point type. The only other operations which require this are the arithmetic operators and the function fma. Other functions, including pow, are not so constrained.

### Example

Run this code

    #include <stdio.h>
    #include <math.h>
    #include <errno.h>
    #include <fenv.h>

    #pragma STDC FENV_ACCESS ON

    int main(void)
    {
        // normal use
        printf("sqrt(100) = %f\n", sqrt(100));
        printf("sqrt(2) = %f\n", sqrt(2));
        printf("golden ratio = %f\n", (1+sqrt(5))/2);
        // special values
        printf("sqrt(-0) = %f\n", sqrt(-0.0));
        // error handling
        errno = 0; feclearexcept(FE_ALL_EXCEPT);
        printf("sqrt(-1.0) = %f\n", sqrt(-1));
        if(errno == EDOM) perror("    errno == EDOM");
        if(fetestexcept(FE_INVALID)) puts("    FE_INVALID was raised");
    }

Possible output:

    sqrt(100) = 10.000000
    sqrt(2) = 1.414214
    golden ratio = 1.618034
    sqrt(-0) = -0.000000
    sqrt(-1.0) = -nan
        errno = EDOM: Numerical argument out of domain
        FE_INVALID was raised

### References

- C11 standard (ISO/IEC 9899:2011):

  - 7.12.7.5 The sqrt functions (p: 249)

  - 7.25 Type-generic math <tgmath.h> (p: 373-375)

  - F.10.4.5 The sqrt functions (p: 525)

- C99 standard (ISO/IEC 9899:1999):

  - 7.12.7.5 The sqrt functions (p: 229-230)

  - 7.22 Type-generic math <tgmath.h> (p: 335-337)

  - F.9.4.5 The sqrt functions (p: 462)

- C89/C90 standard (ISO/IEC 9899:1990):

  - 4.5.5.2 The sqrt function

### See also

pow powf powl (C99)(C99) | computes a number raised to the given power (\(\small{x^y}\)xy) (function)
cbrt cbrtf cbrtl (C99)(C99)(C99) | computes cube root (\(\small{\sqrt[3]{x} }\)3√x) (function)
hypot hypotf hypotl (C99)(C99)(C99) | computes square root of the sum of the squares of two given numbers (\(\scriptsize{\sqrt{x^2+y^2} }\)√x2 +y2 ) (function)
csqrt csqrtf csqrtl (C99)(C99)(C99) | computes the complex square root (function)

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