41.
[tex]a) \ \frac{-\sqrt{3}}{4}-\sqrt{3} = \frac{-\sqrt{3}-4\sqrt{3}}{4} = -\frac{5\sqrt{3}}{4} =-\frac{5}{4}\sqrt{3}\\\\b) \ \frac{\sqrt[3]{5}}{2}+2\sqrt[3]{5} =\frac{\sqrt[3]{5}+4\sqrt[3]{5}}{2} = \frac{5\sqrt[3]{5}}{2} = \frac{5}{2}\sqrt{3}\\\\c) \ \frac{25\sqrt{10}-15}{5} = 5\sqrt{10}-3\\\\d) \ 2\sqrt[3]{5}-2(1+\sqrt[3]{5}) = 2\sqrt[3]{5}-2-2\sqrt[3]{5} =-2[/tex]
43.
[tex]c)\\4\sqrt{2}(5\sqrt{2}-6)+3\sqrt{2}(7-4\sqrt{2}) = 20\cdot2-24\sqrt{2}+21\sqrt{2}-12\cdot2 =40-24-3\sqrt{2} = \\\\=16-3\sqrt{2}\\\\d)\\5(3+2\sqrt[3]{7})-2(3\sqrt[3]{7}-4) = 15+10\sqrt[3]{7}-6\sqrt[3]{7}+8 = 23+4\sqrt[3]{7}[/tex]
48.
[tex]d) \ \frac{4\sqrt{10}\cdot\sqrt{5}}{5\sqrt{2}} =\frac{4}{5}\sqrt{\frac{10\cdot5}{2}}=\frac{4}{5}\sqrt{\frac{50}{2}} = \frac{4}{5}\cdot\sqrt{25} = \frac{4}{5}\cdot5 = 4\\\\h) \ \frac{4\sqrt{6}\cdot2\sqrt{3}}{3\sqrt{2}} = \frac{8}{3}\sqrt{\frac{6\cdot3}{2}} = \frac{8}{3}\sqrt{\frac{18}{2}} = \frac{8}{3}\cdot\sqrt{9} = \frac{8}{3}\cdot3 = 8[/tex]
