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Mathematical finale questions and answers in senior high school entrance examination
This enthusiastic netizen is right, but the answer is too simple. Let me explain it in detail.

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.

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