<em>Regular hexagons have a property that cutting off the triangles obtained by joining the midpoints of consecutive sides leaves a hexagon of 3/4 of the area.</em>
This means the area of each hexagon inside out starting from the one with unit area is 4/3 of the previous one.
If all three radical expressions can be simplified to have a radicand of 3xy, than each original expression has a radicand that is a product of 3xy and a perfect square.