\(\sqrt{160}\cdot\sqrt{10}+\sqrt{8}\cdot\sqrt{0,5}\\ =\sqrt{1600}+\sqrt{8\cdot0,5}\\ =\sqrt{16\cdot100}+\sqrt{4}\\ =4\cdot10+2\\ =40+2\\ =42\\ \sqrt{\left(3-\sqrt{7}\right)^2}+\sqrt{\left(2-\sqrt{7}\right)^2}\\ =\left|3-\sqrt{7}\right|+\left|2-\sqrt{7}\right|\\ =3-\sqrt{7}+\sqrt{7}-2\\ =1\)
\(3\sqrt{50}-4\sqrt{18}+\dfrac{1}{4}\sqrt{32}\\ =3\sqrt{25\cdot2}-4\sqrt{9\cdot2}+\dfrac{1}{4}\sqrt{16\cdot2}\\ =3\cdot5\sqrt{2}-4\cdot3\sqrt{2}+\dfrac{1}{4}\cdot4\sqrt{2}\\ =15\sqrt{2}-12\sqrt{2}+\sqrt{2}\\ =\left(15-12+1\right)\sqrt{2}\\ =4\sqrt{2}\)
\(\dfrac{2+\sqrt{3}}{2-\sqrt{3}}+\dfrac{2-\sqrt{3}}{2+\sqrt{3}}\\ =\dfrac{\left(2+\sqrt{3}\right)^2}{4-3}+\dfrac{\left(2-\sqrt{3}\right)^2}{4-3}\\ =4+4\sqrt{3}+3+4-4\sqrt{3}+3\\ =14\)
