Vì $\sqrt{5-2\sqrt 6} = \sqrt 3 -\sqrt 2;\ \quad 49-20\sqrt 6 =(5-2\sqrt 6)^2$
Tử là $(5+2\sqrt 6)(5-2\sqrt 6)^2 (\sqrt 3-\sqrt 2)=(5+2\sqrt 6)(5-2\sqrt 6) (5-2\sqrt 6)(\sqrt 3-\sqrt 2)=(5-2\sqrt 6)(\sqrt 3-\sqrt 2)$
$=(\sqrt 3-\sqrt 2)^2 (\sqrt 3-\sqrt 2)=(\sqrt 3-\sqrt 2)^3=9\sqrt 3-11\sqrt 2$
Vậy $P=1$