Square Root without using any function

#include <stdio.h>
int main() {
    double num,high, low, mid;
    printf("Please enter a number: \n");
    scanf("%lf", &num);
    low = 0;
    high = num;
    int a = 100;
    while (a--) {
        mid = low + (high-low)/2;
        if (mid*mid > num) high = mid - 10e-7;
        else if (mid*mid < num) low = mid + 10e-7;
        else break;
    }
    printf("Square-Root: %.6lf\n", mid);
    main();
}