a: \(\left(2-\sqrt5\right)\left(2+\sqrt5\right)=4-5=-1\)
b: \(\frac{\sqrt6-6}{\sqrt6-1}+\frac{2\sqrt3+3\sqrt2}{\sqrt2+\sqrt3}\)
\(=-\frac{\sqrt6\left(\sqrt6-1\right)}{\sqrt6-1}+\frac{\sqrt6\left(\sqrt2+\sqrt3\right)}{\sqrt2+\sqrt3}=-\sqrt6+\sqrt6=0\)
c: \(\sqrt{4-2\sqrt3}-\frac{3-2\sqrt3}{\sqrt3-2}\)
\(=\sqrt{\left(\sqrt3-1\right)^2}-\frac{\sqrt3\left(\sqrt3-2\right)}{\sqrt3-2}=\sqrt3-1-\sqrt3=-1\)
d: \(\sqrt{6-2\sqrt5}-\frac{\sqrt5-5}{1-\sqrt5}\)
\(=\sqrt{\left(\sqrt5-1\right)^2}-\frac{\sqrt5\left(1-\sqrt5\right)}{1-\sqrt5}=\sqrt5-1-\sqrt5\)
=-1
e: \(\frac{\sqrt{44}}{\sqrt{11}}-2\sqrt{12}+3\cdot\sqrt{\frac13}+\sqrt{27}\)
\(=\sqrt4-2\cdot2\sqrt3+\sqrt3+3\sqrt3=2\)
f: \(\left(20\sqrt{300}-15\cdot\sqrt{675}+5\cdot\sqrt{75}\right):\sqrt{15}\)
\(=20\cdot\sqrt{20}-15\cdot\sqrt{45}+5\cdot\sqrt5\)
\(=40\sqrt5-45\sqrt5+5\sqrt5=0\)
g: \(\left(\sqrt7-\sqrt{12}-\sqrt{27}\right)\left(\sqrt7+\sqrt{12}+\sqrt{27}\right)\)
\(=\left(\sqrt7-2\sqrt3-3\sqrt3\right)\left(\sqrt7+2\sqrt3+3\sqrt3\right)\)
\(=\left(\sqrt7-5\sqrt3\right)\left(\sqrt7+5\sqrt3\right)=7-75=-68\)
