∵1≤a≤3
∴a-1≥0,a-3≤0
|a-1|=a-1,|a-3|=-(a-3)=3-a,
∴√a²-2a+1+√a²-6a+9
=√(a-1)²+√(a-3)²
=|a-1|+|a-3|
=a-1+3-a
=2