6.
\(P=\sqrt{5^2.3}-\sqrt{3}=5\sqrt{3}-\sqrt{3}=4\sqrt{3}\)
7.
\(2\sqrt{3}+\sqrt{27}=2\sqrt{3}+3\sqrt{3}=5\sqrt{3}=\sqrt{5^2.3}=\sqrt{75}\)
Mà \(\sqrt{75}>\sqrt{74}\Rightarrow2\sqrt{3}+\sqrt{27}>\sqrt{74}\)
b,
\(\left(\dfrac{1}{\sqrt{x}-2}-\dfrac{1}{\sqrt{x}+2}\right).\dfrac{x-4}{4}=\left(\dfrac{\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\dfrac{\sqrt{x}-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right).\dfrac{x-4}{4}\)
\(=\dfrac{4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}.\dfrac{x-4}{4}=\dfrac{4}{x-4}.\dfrac{x-4}{4}=1\)
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