Question

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Answer 1

a) $\left(\frac{8}{5\sqrt{6}}-\frac{4}{\sqrt{24}}-\frac{16}{15\sqrt{6}}\right)-\left(\frac{8}{3\sqrt{54}}-\frac{6}{\sqrt{54}}\right) =\frac{8}{5\sqrt{6}}-\frac{4}{\sqrt{24}}-\frac{16}{15\sqrt{6}}-\left(\frac{8}{3\sqrt{54}}-\frac{6}{\sqrt{54}}\right) =\frac{2^2\sqrt{2}}{5\sqrt{3}}-\sqrt{\frac{2}{3}}-\frac{2^3\sqrt{2}}{15\sqrt{3}}-\left(\frac{4\sqrt{2}}{9\sqrt{3}}-\sqrt{\frac{2}{3}}\right) =\frac{12\sqrt{2}}{15\sqrt{3}}-\frac{2^3\sqrt{2}}{15\sqrt{3}} =\frac{12\sqrt{2}-2^3\sqrt{2}}{15\sqrt{3}} =$

$=-\sqrt{\frac{2}{3}}-\left(\frac{4\sqrt{2}}{9\sqrt{3}}-\sqrt{\frac{2}{3}}\right)+\frac{4\sqrt{2}}{15\sqrt{3}} =-\sqrt{\frac{2}{3}}-\frac{4\sqrt{2}}{9\sqrt{3}}+\sqrt{\frac{2}{3}}+\frac{4\sqrt{2}}{15\sqrt{3}} =-\frac{8\sqrt{2}}{45\sqrt{3}} =-\frac{8\sqrt{6}}{135}$

b) $\left(\frac{9}{2\sqrt{6}}-\frac{8}{3\sqrt{6}}-\frac{4}{\sqrt{6}}\right)-\left(\frac{16}{5\sqrt{16}}-\frac{33}{10\sqrt{6}}\right)-\left(\frac{3}{\sqrt{6}}-\frac{8}{3\sqrt{6}}\right) =\frac{9}{2\sqrt{6}}-\frac{8}{3\sqrt{6}}-\frac{4}{\sqrt{6}}-\left(\frac{16}{5\sqrt{16}}-\frac{33}{10\sqrt{6}}\right)-\left(\frac{3}{\sqrt{6}}-\frac{8}{3\sqrt{6}}\right) =$$=\frac{3\sqrt{3}}{2\sqrt{2}}-\frac{2^2\sqrt{2}}{3\sqrt{3}}-\frac{2\sqrt{2}}{\sqrt{3}}-\left(\frac{4}{5}-\frac{11\sqrt{3}}{10\sqrt{2}}\right)-\left(\sqrt{\frac{3}{2}}-\frac{4\sqrt{2}}{3\sqrt{3}}\right) =\frac{27}{6\sqrt{6}}-\frac{16}{6\sqrt{6}}-\frac{24}{6\sqrt{6}} =\frac{27-16-24}{6\sqrt{6}} =\frac{-13}{6\sqrt{6}} -\left(\frac{4}{5}-\frac{11\sqrt{3}}{10\sqrt{2}}\right)-\left(\sqrt{\frac{3}{2}}-\frac{4\sqrt{2}}{3\sqrt{3}}\right)-\frac{13}{6\sqrt{6}} =$

$=-\frac{4}{5}+\frac{\sqrt{3}\cdot \:11}{10\sqrt{2}}-\sqrt{\frac{3}{2}}+\frac{4\sqrt{2}}{3\sqrt{3}}-\frac{13}{6\sqrt{6}} =\frac{2\left(\sqrt{6}-6\right)}{15}$

c) $\left(\frac{18}{3\sqrt{3}}-\frac{6}{2\sqrt{3}}+\frac{2}{\sqrt{3}}\right)-\left(\frac{12}{\sqrt{3}}+\frac{5}{2\sqrt{3}}-\frac{4}{3\sqrt{3}}\right) =\frac{18}{3\sqrt{3}}-\frac{6}{2\sqrt{3}}+\frac{2}{\sqrt{3}}-\left(\frac{12}{\sqrt{3}}+\frac{5}{2\sqrt{3}}-\frac{4}{3\sqrt{3}}\right) =2\sqrt{3}-\sqrt{3}+\frac{2}{\sqrt{3}}-\left(\frac{7}{6\sqrt{3}}+4\sqrt{3}\right) =2\sqrt{3}-\sqrt{3}+\frac{2}{\sqrt{3}}-4\sqrt{3}-\frac{7}{6\sqrt{3}} =-3\sqrt{3}+\frac{5}{6\sqrt{3}} =-3\sqrt{3}+\frac{5\sqrt{3}}{18}$

d) $\left(\frac{13}{5\sqrt{2}}+\frac{6}{3\sqrt{2}}\right)-\left(\frac{26}{3\sqrt{2}}+\frac{6}{4\sqrt{2}}-\frac{7}{\sqrt{2}}\right) =\frac{13}{5\sqrt{2}}+\frac{6}{3\sqrt{2}}-\left(\frac{26}{3\sqrt{2}}+\frac{6}{4\sqrt{2}}-\frac{7}{\sqrt{2}}\right) =\frac{13}{5\sqrt{2}}+\sqrt{2}-\frac{19}{6\sqrt{2}} =\frac{13}{5\sqrt{2}}-\frac{19}{6\sqrt{2}}+\sqrt{2} =\frac{78}{30\sqrt{2}}-\frac{95}{30\sqrt{2}} =\frac{78-95}{30\sqrt{2}} =\frac{78-95}{30\sqrt{2}} =\frac{-17}{30\sqrt{2}} =\sqrt{2}-\frac{17}{30\sqrt{2}}=$

$=\sqrt{2}-\frac{17\sqrt{2}}{60}$

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