Take the midpoint n of BM and connect it with PN. MN=√2, PM=2, BM=2√2, then there are MN/PM=PM/BM=√2/2, ∴△PMN∽△BMP. According to the similarity ratio, PN=√2/2BP is obtained. The minimum value of BP +√2B' p =√2 (√ 2/2bp+b 'p).
The minimum value of =√2(PN+B'P), and the minimum value of PN+B'P is the length of line segment b' n, so it is easy to find B'N=√( 1? +3? ) =√ 10, √ 2 √ 10 = 2√5. That is, the minimum value of BP+√2B'P is 2 √ 5.