i'm still pretty new to programming in c# but I gave it a shot, probably over complicated things: using System; using System.Collections.Generic; using System.Linq; using System.Text; using System.Threading.Tasks;

namespace Practice_4_12_17 { class Program { static int getVar(out int a, out int b, out int c, out int d) { /* Gets the values to be used / Console.Write("a: "); a = Convert.ToInt32(Console.ReadLine()); Console.Write("b: "); b = Convert.ToInt32(Console.ReadLine()); Console.Write("c: "); c = Convert.ToInt32(Console.ReadLine()); Console.Write("d: "); d = Convert.ToInt32(Console.ReadLine()); return a + b + c + d; } static void Main(string[] args) { Console.WriteLine("Let's simplify an equation:"); Console.WriteLine("Let's start off with an equation in the form of (asqrt(b))/(csqrt(d))"); Console.WriteLine("And let's elimnate the radical in the denominator, thus eliminating the 'd'"); Console.WriteLine("And putting the equation in the form of (asqrt(b))/c"); Console.WriteLine("Naturally, this means that the values for a, b, and c will have to change"); Console.WriteLine("\nPlease enter the values for a, b, c, and d: \n");

        int a, b, c, d;
        //Go to method to obtain values
        getVar(out a, out b, out c, out d);

        //Verify correct values have been input
        Question:
        Console.WriteLine("\n \nSo you want to simplify ({0}*sqrt({1}))/({2}*sqrt({3})) (y/n)? \n", a, b, c, d);
        string ans;
        ans = Console.ReadLine();
        switch (ans)
        {
            case "y":
                break;
            case "n":
                Console.WriteLine();
                getVar(out a, out b, out c, out d);
                goto Question;
            default:
                goto Question;

        }

        //define 2nd instance of variables
        int a2 = a;
        int b2;
        int c2 = c * d;

        //start doing the simplifying

        //find new b (and maybe a)
        int newRad;
        int power = 0;

        newRad = b * d;
        b2 = newRad;

        int newRad2 = newRad;
        double quickCheck = Math.Sqrt(newRad);
        int evenSqrt = 0;
        if (quickCheck % 1 == 0)
        {
            evenSqrt = 1;
            goto A_and_C_Reduction;
        }
    Reduce_Radical:

        double factor = Math.Sqrt(newRad2);
        int reduceIt;
        for(int p = 2; p <= factor; p++)
        {
            int p2 = p * p;
            reduceIt = newRad2 % p2;
            switch (reduceIt)
            {
                case 0:
                    newRad2 /= (p2);
                    power += p;
                    goto Reduce_Radical;
                default:
                    break;
            }
        }
        int power2 = power * power;
        if (power > 0)
        {
            b2 = newRad / power2;
            a2 *= power;
        }

        //find new a and c
        A_and_C_Reduction:

        int reduction = (c/2);

        Bring_It_Down:


        for(int x = 2; x <= reduction; x++)
        {
            if((a2%x == 0) && (c2%x == 0)) 
            {
                a2 /= x;
                c2 /= x;
                goto Bring_It_Down;
            }
        }

        if (c2 != 1)
        {
            switch (evenSqrt)
            {
                case 1:
                    int b3 = Convert.ToInt32(Math.Sqrt(b2));
                    int a3 = a2 * b3;
                    Console.WriteLine("\n'b' and 'd' have been elimnated");
                    Console.WriteLine("a now equals {0} and c now equals {1}\n", a3, c2);
                    Console.WriteLine("Your new radical is: \n\n");
                    Console.WriteLine("({0}/{1})", a3, c2);
                    int divisible = a3 % c2;
                    if (divisible == 0)
                    {
                        int a4 = a3 / c2;
                        Console.WriteLine("'c' was a factor of 'a', as a result the entire number is:");
                        Console.WriteLine(a4);
                    }
                    break;

                default:
                    Console.WriteLine("\n'd' has been elimnated");
                    Console.WriteLine("a now equals {0}, b now equals {1}, and c now equals {2}\n", a2, b2, c2);
                    Console.WriteLine("Your new radical is: \n\n");
                    Console.WriteLine("({0}*sqr({1})/{2}", a2, b2, c2);
                    break;
            }
        }
        else
        {
            Console.WriteLine("\n'c' and'd' have been elimnated");
            Console.WriteLine("('c' is eliminated because it is giving us a denominator of 1");
            Console.WriteLine("a now equals {0}, b now equals {1}, and c now equals {2}", a2, b2, c2);
            if (evenSqrt == 1)
            {
                int a3 = a2 * b2;
                Console.WriteLine("\n'b' has also been elimnated seeing as it equals '1' now");
                Console.WriteLine("the number left over (the entire fraction) is {0}", a3);
            }
            else
            {
                Console.WriteLine("Your new radical is: \n\n");
                Console.WriteLine("({0}*sqr({1})/{2}", a2, b2);
            }
        }

        Console.ReadLine(); 
    }
}

}