# 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` (√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 exact. The only other operations required to be exact are the arithmetic operators and the function fma. After rounding to the return type (using default rounding mode), the result of `sqrt` is indistinguishable from the infinitely precise result. In other words, the error is less than 0.5 ulp. 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 (xy) (function)
cbrt cbrtf cbrtl (C99)(C99)(C99) | computes cubic root (3√x) (function)
hypot hypotf hypotl (C99)(C99)(C99) | computes square root of the sum of the squares of two given numbers (√x2 +y2 ) (function)
csqrt csqrtf csqrtl (C99)(C99)(C99) | computes the complex square root (function)

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