[tex]c)(\sqrt{2}+5\sqrt{\frac{5}{24}}-3\sqrt{\frac{3}{40}}-4\sqrt{\frac{2}{15}})*\sqrt2=\\
(\sqrt2+5\frac{\sqrt5}{2\sqrt6}-3\frac{\sqrt3}{2\sqrt10}-4\frac{\sqrt2}{\sqrt{15}})*\sqrt2=\\
(\sqrt2+\frac{10\sqrt6+\sqrt5}{2\sqrt6}-\frac{6\sqrt{10}+\sqrt3}{2\sqrt{10}}-\frac{4\sqrt{15}+\sqrt2}{\sqrt{15}})*\sqrt2=\\
(\sqrt2+\frac{60+\sqrt{30}}{12}-\frac{60+\sqrt{30}}{20}-\frac{60+\sqrt{30}}{15})*\sqrt2=\\
(\sqrt2+\frac{300+5\sqrt{30}-180-3\sqrt{30}-240-4\sqrt{30}}{60})*\sqrt2=\\
[/tex]
[tex](\sqrt2+\frac{-120-2\sqrt{30}}{60})*\sqrt{2}=\\
(\sqrt{2}-\frac{120+2\sqrt{30}}{60})*\sqrt2=\\
\frac{60\sqrt2-120-2\sqrt{30}}{60}*\sqrt2=\\
\frac{120-120\sqrt2-2\sqrt{60}}{60}=\\
\frac{60-60\sqrt2-\sqrt60}{30}
[/tex]
