\frac 1{n^4}\leq\bigg|\underbrace{P\left(\sqrt 3-\sqrt 2\right)}_{=0}-P\left(\frac m n\right)\bigg|=|P'(\xi)|\bigg|\left(\sqrt 3-\sqrt2\right)-\frac m n\bigg|<20\bigg|\left(\sqrt 3-\sqrt2\right)-\frac m n\bigg|