C++ 无法在for循环中多次打印

我试着写一个程序来获取一个数字的根，例如，如果你在菜单中输入3，它会试图找到你的数字的第三个根，所以如果你输入8，它会给你2，但有一个问题。我正在使用for循环，如果我尝试在循环中为我的条件定义一个else，它将打印cout，打印次数与定义循环的次数相同。我该怎么做才能解决这个问题？有人能帮我吗？我应该改用while吗？请保持你的答案简单明了。 这是我的密码：

system("cls");
    system("color 78");
    int roots;
    cout << "Which root are you trying to find out?" << endl;
    cin >> roots;
    switch (roots)
    {
    case 1:
    {
        system("cls");
        double po;
        cout << "Please enter the number you wnat to see its first root: " << endl;
        cin >> po;
        cout << "Your number's first root is: " << po << endl;
    Backhome();

    }
    break;
    case 2:
    {
    system("cls");
    double p;
    cout <<"Please enter the number you want to find its second root:"<< endl;
    cin >> p;
    cout <<"Your number's second root is: "<< sqrt(p) << endl;
    cout << "Your number's second root is: " << "-" << sqrt(p) << endl;
    Backhome();
    }
    break;
case 3:
{
    system("cls");
    double th;
    cout << "Please enter the number you want to find its third root: "<< endl;
    cin >> th;
    for (int i= -10000 ; i <= 10000; i++)
    {
        if ((i*i*i) == th)
        {
            cout << "Your number's third root is: " << i << endl;
        }
        else
        {
         cout << "Your number doesn't have a third root." << endl;
         }
    }
    Backhome();
}
break;
case 4:
{
    system("cls");
    double foot;
    cout << "Enter the number you want to see its fourth root: " << endl;
    cin >> foot;
    for (int i = -10000; i <= 10000; i++)
    {
        if ((i*i*i*i) == foot)
        {
            cout << "Your number's fourth root is: " << i << endl;
        }
        else
        {
         cout << "Your number doesn't have a fourth root." << endl;
         }
    }
    Backhome();
}
break;
case 5:
{
    system("cls");
    double pive;
    cout << "Enter the number you want to see its fifth root: " << endl;
    cin >> pive;
    for (int i = -10000; i <= 10000; i++)
    {
        if ((i*i*i*i*i) == pive)
        {
            cout << "Your number's fifth root is: " << i << endl;
        }

        else
        {
         cout << "Your number doesn't have a fifth root." << endl;
         }
}
    Backhome();
}

系统（“cls”）；
系统（“颜色78”）；
int根；
库特根；
开关（根）
{
案例1：
{
系统（“cls”）；
双坡；
库特波；
cout您的程序可能会很短，您只需将数字加1/根：

system("cls");
system("color 78");
int roots;
cout << "Which root are you trying to find out?" << endl;
cin >> roots;    
system("cls");
double po;
cout << "Please enter the number you wnat to see its " << roots << "th root: " << endl;
cin >> po;
cout << "Your number's " << roots << "th root is: " << pow(po, 1.0/roots) << endl;
Backhome(); 

系统（“cls”）；
系统（“颜色78”）；
int根；
库特根；
系统（“cls”）；
双坡；
cout您的程序可能会很短，您只需将数字加1/根：

system("cls");
system("color 78");
int roots;
cout << "Which root are you trying to find out?" << endl;
cin >> roots;    
system("cls");
double po;
cout << "Please enter the number you wnat to see its " << roots << "th root: " << endl;
cin >> po;
cout << "Your number's " << roots << "th root is: " << pow(po, 1.0/roots) << endl;
Backhome(); 

系统（“cls”）；
系统（“颜色78”）；
int根；
库特根；
系统（“cls”）；
双坡；
库特