Playing with Powers - Rachel's thoughts

Thank you to Rachel for sending us her thoughts on Playing with Powers.

1. 9² + 3² = 90
   6² + 12² = 180
   57² + 63² = 2406
    
2. Both the pairs of numbers in each sum are a multiple of three to start with, before they have been squared.
    
3. It works because when you multiply a multiple of three by itself its still a multiple of three and when you add two multiples of three together the sum is still divisible by three.
    
4. 12² + 16² = 400
   36² + 44² = 3,232
   444² + 336 = 310,032
    
5. Both of the pairs of numbers in each sum are a multiple of 4 to start with before they have been squared.
    
6. It works because when you multiply a multiple of four by itself its still a multiple of four and when you add two multiples of four together the sum will still divide by four.
    
7. 5² + 65² = 4,250
   15² + 585² = 342,450
   45² + 95000² = 9,025,002,025