a: \(A=\sqrt{27}-2\sqrt{48}+3\sqrt{75}\)
\(=3\sqrt3-2\cdot4\sqrt3+3\cdot5\sqrt3\)
\(=3\sqrt3-8\sqrt3+15\sqrt3=10\sqrt3\)
b: \(B=\sqrt{\left(\sqrt5-2\right)^2}-\sqrt{\left(\sqrt5-3\right)^2}\)
\(=\sqrt5-2-\left|3-\sqrt5\right|\)
\(=\sqrt5-2-\left(3-\sqrt5\right)=2\sqrt5-5\)
c: \(C=\sqrt{\left(2\sqrt3+1\right)^2}+\sqrt{\left(2\sqrt3-5\right)^2}\)
\(=2\sqrt3+1+5-2\sqrt3\)
=5+1
=6
d: \(D=\sqrt{9-4\sqrt5}-\sqrt{14+6\sqrt5}\)
\(=\sqrt{\left(\sqrt5-2\right)^2}-\sqrt{\left(3+\sqrt5\right)^2}\)
\(=\sqrt5-2-3-\sqrt5=-5\)
e: \(E=\frac{4}{\sqrt5-2}-\frac{32}{\sqrt5+1}\)
\(=\frac{4\left(\sqrt5+2\right)}{\left(\sqrt5-2\right)\left(\sqrt5+2\right)}-\frac{32\left(\sqrt5-1\right)}{\left(\sqrt5+1\right)\left(\sqrt5-1\right)}\)
\(=4\left(\sqrt5+2\right)-8\left(\sqrt5-1\right)=4\sqrt5+8-8\sqrt5+8=16-4\sqrt5\)
