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Irrational Arithmagons

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

This problem builds on the ideas in Multiplication Arithmagons.
 
In a multiplication arithmagon, the number on each edge of the arithmagon is the product of the numbers at the adjacent vertices.
 
Can you work out the numbers that belong in the circles to make this multiplication arithmagon correct?
arithmagon with -6 + 2 root 2, 7 + 7 root 2, 2 - 4 root 2