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probably a binary search would also work
for ex
2<sqrt(8)<3;
now try 2.5 since 2.5*2.5=6.25 so try betwen 2.5 and 3 and so on

use rahsonmethod
float x1=num,x2=0;
x2=.5*(x1+num/x1);
while((x1-x2)!=0)
{
x1=x2;
x2=.5*(x1+num/x1);
}
cout<<x2;

public static void SquareRoot(int n)
        {
            float guess = 1;
            float number = (float)n;
            while (Math.Abs((number / guess) - guess) > 0.001f)
            {
                guess = (guess + (number / guess)) / 2;
            }
            Console.WriteLine("Square Root of " + n + ": " + guess);
        }

find an integer i, such that i*i < float < (i+1)*(i+1)
then, denote x = (f-i*i)/(i*i)
sqrt(f) = i* (1+x)^0.5
then Taylor series.

From a mathematical point of view.

you can also do it as if you are solving an equation:
x^2 - f = 0;

using either Newton's recursive method;

void prob6()
{
	float input;
	cout<<"Input a non-negative float number!"<<endl;
	cin>>input;
	while(input<0) //if it is negative, re-input
	{
		cin>>input;
	}

	//Find an initial point x0, such that x0^2>input and x0 is minimal
	int i=0;
	while(true)
	{
		if(i*i>input)
			break;
		i++;
	}

	float x_0=(float)i;
	float x_1;
	float error=0.01f;
	float diff;
	while(true)
	{
		x_1=x_0-(x_0*x_0-input)/(2*x_0);
		diff=x_1*x_1-input;
		if((diff<error)||(diff>-error))
		   break;
		else
		   x_0=x_1;
		
	}

	cout<<"The approximate (Error<="<<error<<")square-root is:"<<x_1<<endl;
}

double (int num,int tol) //num = number,tol=tolerance value
{
double tmp=num,tmp2;
while(1)
{
tmp2=.5*(tmp+num/tmp);
if(tmp - tmp2 < tol)
{
return tmp2;
}
tmp=tmp2;
}
}

#include <iostream>
using namespace std;

static double root;
static double diff;

void getroot(double num,double min, double max)
{
root=(min+max)/2;
diff=root*root-num;
if(0<=diff)
{
if(diff<0.001)
cout<<root;
else
{
max=root;
getroot(num,min,max);
}
}
else
{
min=root;
getroot(num,min,max);
}


}

int main(){
double num;

cout<<"please input the number:"<<endl;
cin>>num;
if(num<1)
getroot(num,num,1);
else
getroot(num,0,num);

}

public static double getSqrt(double x) {
double a = 1;
double b = 0;
while(true) {
b = 0.5 * (a + x/a);
if (a == b) break;
a = b;
}
//floating-precision of 4 decimal places
b = (double)(int)((b+0.00005)*10000.0)/10000.0;
return b;
}

double sqrt( int n )
{
	double a = (double) n;
	double x = 1;
 
	for( int i = 0; i < n; i++)
	{
		x = 0.5 * ( x+a / x );
	}
 
	return x;
}

const double epsilon = 0.00000000000000001;
double sqrt(const double x){
if (x < 0){
throw Exception("wrong input");
}

if (abs(x - 1) < epsilon)
return 1;

double left, mid, right;
if (x < 1){
left = x;
right = 1;
}
else{
left = 1;
right = x;
}
mid = (left + right)/2;

while (abs(mid * mid - x) > epsilon){
if (contains(left, mid, x)
right = mid;
else
left = mid;
mid = (left + right)/2;
}

return mid;

}

int contains(double left, double right, double key){
return (key >= left || key <= right)? 1: 0;
}

#include <iostream>
using namespace std;

/* Function declarations */
double mySqrt(double input);
/* Function definitions */
double mySqrt(double input)
{

double result=0.001;
while(result*result - input < 0.0 )
{
result+=0.001;
}
return result;
}

int main()
{
char key;
double result;
double input=5.67;
result=mySqrt(input);
cout<<result<<endl;
cin>>key;
return 0;
}

<pre lang="" line="1" title="CodeMonkey95907" class="run-this">public void square_root (float num) {
float n1 = 0f;
float n2 = 0f;

n1 = num/2;

/Newton-Raphson's method
while(n1 != n2) {
n1 = n2;
n1 = n2 + (((n2*n2) - num)/(2*n2));
}

System.out.println("Square root is " + n1);
}</pre><pre title="CodeMonkey95907" input="yes">
</pre>

Help.......How to stop and make stable of this output....it keeps on giving output...

#include<stdio.h>
main()
{ int i,j,k=1;
long double a,num,n;
printf("Enter the no whose square root is to find\n");
scanf("%Lf",&n);
i=0;
while(i*i<n)
i++;
a=(double)i-1.000;
printf("\n i is %d, %Lf\n",i,a);
while(a*a<n+1)
{
if(a*a==n)
break;
else
{ if(a*a<n)
a=a+1/(pow(10,k));
else
{ a=a-1/(pow(10,k));
k++;
}
}
printf("The square root of %Lf is %Lf\n",n,a);
}
}

enum Status {kValid = 0, kInvalid};
int g_nStatus = kValid;
float sqrf(const float input)
{
g_nStatus = kInvalid;
double base = 0.0;
if(input >= 0){
float tryNum = 1.0;
int i = 0;
int count = 0;
while(i < 8)
{
count = 0;
float midResult = 0.0;
while(midResult < input)
{
base = base + tryNum;
midResult = base * base;
count ++；
}
base = base - tryNum;
tryNum = tryNum / 10.0;
i++;
}
base = base - count * 0.0000001;
if(count > 5);
base = base + 0.000001;
g_nStatus = kValid;
}
return (float)base;
}

public int sqrt(int x) {
    if(x<0) return -1;
    if(x==0) return 0;
    int l=1;
    int r=x/2+1;
    while(l<=r)
    {
        int m = (l+r)/2;
        if(m<=x/m && x/(m+1)<m+1)
            return m;
        if(x/m<m)
        {
            r = m-1;
        }
        else
        {
            l = m+1;
        }
    }
    return 0;
}