a,  \(1< 2\Rightarrow\sqrt{1}< \sqrt{2}\Rightarrow1+1< \sqrt{2}+1\Rightarrow2< \sqrt{2}+1\)

c, \(4>3=>\sqrt{4}>\sqrt{3}=>\sqrt{4}-1>\sqrt{3}-1\Rightarrow1>\sqrt{3}-1\)

d, \(16>11=>\sqrt{16}>\sqrt{11}\Rightarrow4>\sqrt{11}=>4.\left(-3\right)< \sqrt{11}.\left(-3\right)\)

\(=>-12< -3.\sqrt{11}\) 

\(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+........+\frac{1}{\sqrt{2007}+\sqrt{2008}}\)

\(=\frac{1-\sqrt{2}}{1-2}+\frac{\sqrt{2}-\sqrt{3}}{2-3}+........+\frac{\sqrt{2007}-\sqrt{2008}}{2007-2008}\)

\(=\frac{1-\sqrt{2}+\sqrt{2}-\sqrt{3}+..........+\sqrt{2007}-\sqrt{2008}}{-1}\)

\(=\frac{1-\sqrt{2008}}{-1}=\sqrt{2008-1}\)

\(\sqrt{\frac{149^2-76^2}{457^2-384^2}}=\sqrt{\frac{73.225}{73.841}}=\sqrt{\frac{225}{841}}=\frac{\sqrt{225}}{\sqrt{841}}=\frac{15}{29}\)