AB ratio AE=ED ratio DF;

So the length of DF is1;

Take the midpoint p of BD;

Then EP = 2；;

EP:DF = 2: 1；

So pg: GD = 2:1;

That is, DG =1/3 * DG =1/6 * BD;

DG= 1/6* quadruple root number two;

That is, two-thirds of the root number two.