a: Ta có: \(A=\left(\sqrt{72}-3\sqrt{24}+5\sqrt8\right)\cdot\sqrt2+4\sqrt{27}\)
\(=\left(6\sqrt2+5\cdot2\sqrt2-3\cdot2\sqrt6\right)\cdot\sqrt2+4\cdot3\sqrt3\)
\(=\left(16\sqrt2-6\sqrt6\right)\cdot\sqrt2+12\sqrt3=32-6\sqrt{12}+12\sqrt3\)
=32
b: \(B=\frac{1}{\sqrt2-1}+\frac{14}{3+\sqrt2}\)
\(=\frac{\sqrt2+1}{\left(\sqrt2-1\right)\left(\sqrt2+1\right)}+\frac{14\left(3-\sqrt2\right)}{\left(3+\sqrt2\right)\left(3-\sqrt2\right)}\)
\(=\sqrt2+1+\frac{14\left(3-\sqrt2\right)}{9-2}=\sqrt2+1+2\left(3-\sqrt2\right)\)
\(=\sqrt2+1+6-2\sqrt2=7-\sqrt2\)
c: \(C=\frac{5+3\sqrt5}{\sqrt5}+\frac{3+\sqrt3}{\sqrt3+1}-\left(\sqrt5+3\right)\)
\(=\frac{\sqrt5\left(3+\sqrt5\right)}{\sqrt5}+\frac{\sqrt3\left(\sqrt3+1\right)}{\sqrt3+1}-\left(3+\sqrt5\right)\)
\(=3+\sqrt5+\sqrt3-3-\sqrt5=\sqrt3\)
d: \(D=\sqrt{\left(1-\sqrt2\right)^2}-3\sqrt{18}+4\sqrt{\frac12}\)
\(=\sqrt2-1-3\cdot3\sqrt2+2\sqrt2\)
\(=3\sqrt2-9\sqrt2-1=-6\sqrt2-1\)
e: \(E=\frac{30}{\sqrt6+1}+\frac{2}{\sqrt6-2}-\frac{6}{3-\sqrt6}\)
\(=\frac{30\left(\sqrt6-1\right)}{\left(\sqrt6+1\right)\left(\sqrt6-1\right)}+\frac{2\left(\sqrt6+2\right)}{\left(\sqrt6-2\right)\left(\sqrt6+2\right)}-\frac{6\left(3+\sqrt6\right)}{\left(3-\sqrt6\right)\left(3+\sqrt6\right)}\)
\(=6\left(\sqrt6-1\right)+\sqrt6+2-2\left(3+\sqrt6\right)\)
\(=6\sqrt6-6+\sqrt6+2-6-2\sqrt6=5\sqrt6-10\)
