a) \(A=\sqrt{\left(2-\sqrt{3}\right)^2}+2\sqrt{3}\)
\(A=\left|2-\sqrt{3}\right|+2\sqrt{3}\)
\(A=2-\sqrt{3}+2\sqrt{3}\)
\(A=2+\sqrt{3}\)
b) \(B=\sqrt{18}-2\sqrt{50}+3\sqrt{8}+\sqrt[3]{27}\)
\(B=\sqrt{3^2\cdot2}-2\sqrt{5^2\cdot2}+3\sqrt{2^2\cdot2}+\sqrt[3]{3^3}\)
\(B=3\sqrt{2}-10\sqrt{2}+6\sqrt{2}+3\)
\(B=\left(3-10+6\right)\sqrt{3}+3\)
\(B=3-\sqrt{3}\)
c) \(C=\dfrac{4}{\sqrt{5}-1}-\dfrac{10}{\sqrt{5}}+\dfrac{\sqrt{125}}{\sqrt{5}}+\sqrt{2}\cdot\sqrt{\dfrac{5}{2}}\)
\(C=\dfrac{4\left(\sqrt{5}+1\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}+1\right)}-\dfrac{2\sqrt{5}\cdot\sqrt{5}}{\sqrt{5}}+\sqrt{\dfrac{125}{5}}+\sqrt{2\cdot\dfrac{5}{2}}\)
\(C=\dfrac{4\left(\sqrt{5}+1\right)}{4}-2\sqrt{5}+\sqrt{25}+\sqrt{5}\)
\(C=\sqrt{5}+1-2\sqrt{5}+5+\sqrt{5}\)
\(C=6\)
