How To Loop Questions In C#

I don't really know what you're talking about (what's this about a side length?) but you can square the answers easily enough with:

           for (int i = 0; i < 15; i++)
           {
               questions[i] = i.ToString();
               answers[i] = (i * i).ToString();
           }

Suppose you have:

1.  two buttons - btnStart to load the first question and btnSubmit to submit an answer.
2,  two textboxes - txtQuestion to display the question and txtAnswer for the user to enter the answer, before pressing btnSubmit.

Then the code you'll need for your main form, Form1 say, is as follows:

namespace WindowsFormsApplication1
{
   public partial class Form1 : Form
   {
       public Form1()
       {
           InitializeComponent();
       }


       // private fields
       private string[] questions;
       private string[] answers;
       private bool[] alreadyAsked;
       private Random r = new Random();
       private int numCorrect = 0;
       private int numAsked = 0;
       private int numQuestion = 0;


       private void Form1_Load(object sender, EventArgs e)
       {
           questions = new string[15];
           answers = new string[15];
           alreadyAsked = new bool[15];
           // populate questions & answers (numbers used for testing)
           for (int i = 0; i < 15; i++)
           {
               questions[i] = i.ToString();
               answers[i] = i.ToString();
           }
         
       }


       private void GetNextQuestion()
       {
           while (true)
           {
               int num = r.Next(0, 15);
               if (!alreadyAsked[num])
               {
                   alreadyAsked[num] = true;
                   numQuestion = num;
                   txtQuestion.Text = questions[num];
                   txtAnswer.Focus(); 
                   return;                
               }
           }
       }


       private void btnStart_Click(object sender, EventArgs e)
       {
            btnStart.Enabled = false;
            GetNextQuestion();
       }


       private void btnSubmit_Click(object sender, EventArgs e)
       {
           string answer = txtAnswer.Text.Trim();
           if (answer == "")
           {
               MessageBox.Show("You haven't answered it yet!");
               txtAnswer.Focus();
               return;
           }
         
           if (answer == answers[numQuestion])
           {
               MessageBox.Show ("That's correct!");
               numCorrect++;
           }
           else
           {
               MessageBox.Show("Sorry, that's wrong :(");
           }


           numAsked++;
           txtQuestion.Text = "";
           txtAnswer.Text = "";


           if (numAsked == 15)
           {
               MessageBox.Show(String.Format("You got {0} question(s) correct", numCorrect));
               this.Close();
           }
           else
           {
               GetNextQuestion();
           }
       }
   } 
}

Here's the same code adjusted so that you don't ask the same question more than once:

The code will be something like this:

     string[] questions = new string[15];
      string[] answers = new string[15];
      // populate questions & answers


      Random r = new Random();
      int numCorrect = 0;


      for(int i = 0; i < 15; i++)
      {
         int num = r.Next(0, 15);
         Console.WriteLine(questions[num]);
         string answer = Console.ReadLine();
         if (answer == answers[num])
         {
            Console.WriteLine("That's correct!");
            numCorrect++;
         }
         else
         {
            Console.WriteLine("Sorry, that's wrong :(");
         }
         Console.WriteLine(); 
      }

     Console.WriteLine("You got {0} question(s) correct", numCorrect);

You didn't say whether you wanted to avoid asking the same question more than once but, if you do, then that's easy to adjust for.