a: \(\sqrt{45}-2\cdot\sqrt{80}+\sqrt{1.44\cdot50}\)
\(=3\sqrt5-2\cdot4\sqrt5+\sqrt{72}\)
\(=-5\sqrt5+6\sqrt2\)
c: \(\sqrt{8+2\cdot\sqrt{6-\sqrt{20}}}\)
\(=\sqrt{8+2\cdot\sqrt{\left(\sqrt5-1\right)^2}}=\sqrt{8+2\left(\sqrt5-1\right)}\)
\(=\sqrt{6+2\sqrt5}=\sqrt{\left(\sqrt5+1\right)^2}=\sqrt5+1\)
e: \(\frac{4}{\sqrt5-1}+\frac{3}{\sqrt5-2}+\frac{16}{\sqrt5-3}\)
\(=\frac{4\left(\sqrt5+1\right)}{\left(\sqrt5+1\right)\left(\sqrt5-1\right)}+\frac{3\left(\sqrt5+2\right)}{\left(\sqrt5-2\right)\left(\sqrt5+2\right)}-\frac{16\left(3+\sqrt5\right)}{\left(3-\sqrt5\right)\left(3+\sqrt5\right)}\)
\(=\frac{4\left(\sqrt5+1\right)}{4}+\frac{3\left(\sqrt5+2\right)}{1}-\frac{16\left(3+\sqrt5\right)}{4}=\sqrt5+1+3\sqrt5+6-4\left(3+\sqrt5\right)\)
\(=4\sqrt5+7-12-4\sqrt5=7-12=-5\)
