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

- 9
^{2 }+ 3^{2 }= 90

6^{2 }+ 12^{2 }= 180

57^{2 }+ 63^{2 }= 2406

- Both the pairs of numbers in each sum are a multiple of three to start with, before they have been squared.

- 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.

- 12
^{2 }+ 16^{2 }= 400

36^{2 }+ 44^{2 }= 3,232

444^{2 }+ 336 = 310,032

- Both of the pairs of numbers in each sum are a multiple of 4 to start with before they have been squared.

- 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.

- 5
^{2 }+ 65^{2 }= 4,250

15^{2 }+ 585^{2 }= 342,450

45^{2 }+ 95000^{2 }= 9,025,002,025

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