(20 13? As shown in the figure, it is known that the side length of the square ABCD is 2, the diagonal AC and BD intersect at point O, and the AE bisector ∠BAC and BD intersect at point E, then BE.

∵ quadrilateral ABCD is a square,

∴AO⊥BD,AO=OB=OC=OD，

Then from Pythagorean theorem: 2AO2=22,

AO=OB=2，

∵EM⊥AB，BO⊥AO，AE ∠CAB

∴EM=EO，

From Pythagorean theorem: AM=AO=2,

∫ square ABCD,

∴∠MBE=45 =∠MEB，

∴BM=ME=OE，

In Rt△BME, from Pythagorean theorem, 2ME2=BE2,

That is, 2(2-2)2=BE2,

BE=22-2，

So the answer is: 22-2.