Responses from students:
- Perfect square is when 2 numbers of the same value is times together. Thus as long as 504xk can be square rooted, it is a perfect square. Hence there is more than one possible value of k.
- To find the square root of a perfect square, I must split its prime factors into 2 equal groups. So to make a number that is not a perfect into a perfect square, I must make sure the prime numbers can split into 2 groups without splitting themselves. And since there are many ways to do that, therefroe the many possible values of k.
- To get a perfect square, you must be able to square the index notation of the number. The index notation of 504k can be written as 2^2 x 3^2 x 7^2 and 2^4 x 3^2 x 7^2, and both of them can be squared. Thus, k has more than 1 possible value.
- Any whole number multiplied by itself will give a perfect square but when you multiple the number by itself and multiply it again with a perfect square, you will get a perfect square so it is possible to have more than one possible value of k.
- First divide the index notation into 2 groups, both groups must have equal value so as the groups has the same value, the value can be unlimited and thus "k" can be more than 1 answer when multiplied by 504 to get a square number.
- It is because there are more than one number when times with the power, can be squared as the power is able to be divided into two groups.
- Among the infinite number of multiples of 504, there are bound to be perfect squares among them.
- The square root of these numbers are actually multiples of 504, so as the number of multiples of 504 continues, so does the square root of the multiples of 504.