a: \(A=\left(\sqrt{28}-2\sqrt{14}+\sqrt7\right)\cdot\sqrt7+7\sqrt8\)
\(=\left(2\sqrt7+\sqrt7\right)\cdot\sqrt7-2\sqrt{14}\cdot\sqrt7+7\cdot2\cdot\sqrt2\)
\(=3\sqrt7\cdot\sqrt7-14\sqrt2+14\sqrt2=3\cdot7=21\)
b: \(B=2\sqrt2\left(\sqrt3-2\right)+\left(1+2\sqrt2\right)^2-2\sqrt6\)
\(=2\sqrt6-4\sqrt2+9+4\sqrt2-2\sqrt6\)
=9
c: \(C=\sqrt{4+\sqrt7}\cdot\sqrt{4-\sqrt7}\)
\(=\sqrt{\left(4+\sqrt7\right)\left(4-\sqrt7\right)}\)
\(=\sqrt{16-7}=\sqrt9=3\)
d: \(D=\left(\frac{3}{3-\sqrt2}-\frac{1}{3+\sqrt2}\right)\left(3-2\sqrt2\right)\)
\(=\frac{3\left(3+\sqrt2\right)-\left(3-\sqrt2\right)}{\left(3-\sqrt2\right)\left(3+\sqrt2\right)}\left(3-2\sqrt2\right)\)
\(=\frac{9+3\sqrt2-3+\sqrt2}{7}\cdot\left(3-2\sqrt2\right)=\frac{6+4\sqrt2}{7}\cdot\left(3-2\sqrt2\right)\)
\(=\frac{2\left(3+2\sqrt2\right)\left(3-2\sqrt2\right)}{7}=\frac27\)
e: \(E=\left(\frac{4}{\sqrt5-2}-\frac{11}{2\sqrt5-3}\right)\left(2\sqrt5-5\right)\)
\(=\left(\frac{4\left(\sqrt5+2\right)}{\left(\sqrt5-2\right)\left(\sqrt5+2\right)}-\frac{11\left(2\sqrt5+3\right)}{\left(2\sqrt5-3\right)\left(2\sqrt5+3\right)}\right)\left(2\sqrt5-5\right)\)
\(=\left\lbrack\frac{4\left(\sqrt5+2\right)}{5-4}-\frac{11\left(2\sqrt5+3\right)}{20-9}\right\rbrack\left(2\sqrt5-5\right)\)
\(=\left(4\sqrt5+8-2\sqrt5-3\right)\left(2\sqrt5-5\right)=\left(2\sqrt5+5\right)\left(2\sqrt5-5\right)\)
=20-25
=-5
f: \(F=\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}+\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}\)
\(=\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)}}+\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{\left(5+\sqrt{21}\right)\left(5-\sqrt{21}\right)}}\)
\(=\sqrt{\frac{\left(5-\sqrt{21}\right)^2}{25-21}}+\sqrt{\frac{\left(5+\sqrt{21}\right)^2}{25-21}}=\frac{\sqrt{\left(5-\sqrt{21}\right)^2}+\sqrt{\left(5+\sqrt{21}\right)^2}}{2}\)
\(=\frac{5-\sqrt{21}+5+\sqrt{21}}{2}=\frac{10}{2}=5\)
