Đáp án:
$P=5-\sqrt{3}$
Giải thích các bước giải:
$1)P=\sqrt{7-4\sqrt{3}}+\sqrt[3]{(a+3)\sqrt{a}-3a-1}:\left(\dfrac{a-4}{3(\sqrt{a}-2)}-1\right)\\ =\sqrt{4-2.2.\sqrt{3}+3}+\sqrt[3]{a\sqrt{a}-3a+3\sqrt{a}-1}:\dfrac{a-4-3(\sqrt{a}-2)}{3(\sqrt{a}-2)}\\ =\sqrt{(2-\sqrt{3})^2}+\sqrt[3]{(\sqrt{a}-1)^3}:\dfrac{a-3\sqrt{a}+2}{3(\sqrt{a}-2)}\\ =2-\sqrt{3}+(\sqrt{a}-1):\dfrac{(\sqrt{a}-2)(\sqrt{a}-1)}{3(\sqrt{a}-2)}\\ =2-\sqrt{3}+(\sqrt{a}-1).\dfrac{3}{\sqrt{a}-1}\\ =2-\sqrt{3}+3\\ =5-\sqrt{3}$
