a) \(A=3\sqrt{8}-\sqrt{18}-5\sqrt{\frac{1}{2}}+\sqrt{50}\)
\(=3.2\sqrt{2}-3\sqrt{2}-\frac{5}{2}\sqrt{2}+5\sqrt{2}\)
\(=\frac{11\sqrt{2}}{2}\)
b) \(B=\frac{2}{\sqrt{2}}-\frac{1}{\sqrt{3}-\sqrt{2}}+\frac{2}{\sqrt{3}-1}\)
\(=\sqrt{2}-\frac{\sqrt{3}+\sqrt{2}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}+\frac{2\left(\sqrt{3}+1\right)}{\left(\sqrt{3}\right)^2-1^2}\)
\(=\sqrt{2}-\left(\sqrt{3}+\sqrt{2}\right)+\left(\sqrt{3}+1\right)\)
\(=\sqrt{2}-\sqrt{3}-\sqrt{2}+\sqrt{3}+1\)
\(=1\)
c) \(C=\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
\(=\sqrt{\left(2+\sqrt{3}\right)^2}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
\(=2+\sqrt{3}-\left(2-\sqrt{3}\right)\)
\(=2+\sqrt{3}-2+\sqrt{3}\)
\(=2\sqrt{3}\)
d) \(D=\sqrt{72}+4,5\sqrt{2\frac{2}{3}}-\sqrt{5\frac{1}{3}}+2\sqrt{27}\)
\(=6\sqrt{2}+3\sqrt{6}-\frac{4\sqrt{3}}{3}+6\sqrt{3}\)
\(=6\sqrt{2}+3\sqrt{6}+\frac{14\sqrt{3}}{3}\)
