C sqrt() Function
Definition
In C, sqrt() returns the square root of x. sqrt(4) is 2, and sqrt(0) is 0.
You pass one double, and it must be 0 or greater. The result is a non-negative double. Include <math.h>.
Syntax
Pass a number that is 0 or greater. Start with this call.
| Call | What it does |
|---|
sqrt(4.0) | Returns 2. |
Include <math.h>. On GCC, link with -lm.
Library declarations
double sqrt(double x);
float sqrtf(float x);
long double sqrtl(long double x);
Parameters
| Parameter | Description |
|---|
| x | Required. A double that is 0 or greater. |
Return Value
| Return Value | Description |
|---|
| Square root | A non-negative double. sqrt(4) is 2. |
| NaN | Returned when x is negative. |
C Examples
Example 1 — Perfect and Irrational Roots
Print square roots for common values, including √2.
#include <math.h>
#include <stdio.h>
int main(void) {
printf("sqrt(0) = %.4f\n", sqrt(0.0));
printf("sqrt(9) = %.4f\n", sqrt(9.0));
printf("sqrt(2) = %.5f\n", sqrt(2.0));
printf("sqrt(25) = %.4f\n", sqrt(25.0));
return 0;
}
sqrt(0) = 0.0000
sqrt(9) = 3.0000
sqrt(2) = 1.41421
sqrt(25) = 5.0000
How It Works
- Include math.h. Declares
sqrt; link with -lm on GCC. - Zero and perfect squares.
sqrt(0) is 0; sqrt(9) is 3. - Irrational root.
sqrt(2) is irrational ≈ 1.41421. - Non-negative return. You always get
y >= 0.
Example 2 — Distance with sqrt
Classic 3-4-5 triangle. For production code, prefer hypot when values can be large.
#include <math.h>
#include <stdio.h>
int main(void) {
double a = 3.0;
double b = 4.0;
double d = sqrt(a * a + b * b);
printf("distance = %.1f\n", d);
printf("hypot = %.1f\n", hypot(a, b));
return 0;
}
distance = 5.0
hypot = 5.0
How It Works
- Square the legs.
3² + 4² = 25. - Take sqrt.
sqrt(25) is 5. - Same with hypot.
hypot(3, 4) also returns 5. - Why hypot? It avoids overflow when
a*a + b*b is huge.
Example 3 — Guard Against Negatives
Check the domain before calling sqrt so you never print NaN by accident.
#include <math.h>
#include <stdio.h>
int main(void) {
double x = -4.0;
if (x < 0.0) {
printf("domain error: x must be >= 0\n");
} else {
printf("sqrt(%.1f) = %.4f\n", x, sqrt(x));
}
return 0;
}
domain error: x must be >= 0
How It Works
- Validate first.
x = -4 is outside the domain. - Skip sqrt. Calling it would produce
NaN. - Report clearly. A message is easier to debug than a quiet NaN.
- Optional errno. See
errno.h for EDOM handling.
Frequently Asked Questions
sqrt() returns the square root of x. sqrt(4) is 2, and sqrt(0) is 0.
x is required. It must be a double that is 0 or greater.
A non-negative double. A negative x returns NaN.
Include <math.h>. On GCC, link with -lm.
It returns NaN. The square root of a negative number is not a real result.
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