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\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{7}{3}\times \frac{7}{3}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Add \frac{1}{3} and 2 to get \frac{7}{3}.
\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{2+\frac{1}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Multiply \frac{7}{3} and \frac{7}{3} to get \frac{49}{9}.
\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{\frac{49}{9}}{\frac{5}{2}}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Add 2 and \frac{1}{2} to get \frac{5}{2}.
\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{49}{9}\times \frac{2}{5}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Divide \frac{49}{9} by \frac{5}{2} by multiplying \frac{49}{9} by the reciprocal of \frac{5}{2}.
\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{5}{6}+\frac{3}{2}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Multiply \frac{49}{9} and \frac{2}{5} to get \frac{98}{45}.
\sqrt{6\left(\frac{5}{13}\left(\frac{\frac{98}{45}}{\frac{7}{3}}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Add \frac{5}{6} and \frac{3}{2} to get \frac{7}{3}.
\sqrt{6\left(\frac{5}{13}\left(\frac{98}{45}\times \frac{3}{7}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Divide \frac{98}{45} by \frac{7}{3} by multiplying \frac{98}{45} by the reciprocal of \frac{7}{3}.
\sqrt{6\left(\frac{5}{13}\left(\frac{14}{15}+1-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Multiply \frac{98}{45} and \frac{3}{7} to get \frac{14}{15}.
\sqrt{6\left(\frac{5}{13}\left(\frac{29}{15}-\frac{1}{5}\right)-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Add \frac{14}{15} and 1 to get \frac{29}{15}.
\sqrt{6\left(\frac{5}{13}\times \frac{26}{15}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Subtract \frac{1}{5} from \frac{29}{15} to get \frac{26}{15}.
\sqrt{6\left(\frac{2}{3}-\frac{1}{2}\right)\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Multiply \frac{5}{13} and \frac{26}{15} to get \frac{2}{3}.
\sqrt{6\times \frac{1}{6}\times \left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Subtract \frac{1}{2} from \frac{2}{3} to get \frac{1}{6}.
\sqrt{\left(\frac{5}{9}\times \frac{\frac{2}{15}+\frac{5}{3}}{\frac{5}{2}}\right)^{2}}
Multiply 6 and \frac{1}{6} to get 1.
\sqrt{\left(\frac{5}{9}\times \frac{\frac{9}{5}}{\frac{5}{2}}\right)^{2}}
Add \frac{2}{15} and \frac{5}{3} to get \frac{9}{5}.
\sqrt{\left(\frac{5}{9}\times \frac{9}{5}\times \frac{2}{5}\right)^{2}}
Divide \frac{9}{5} by \frac{5}{2} by multiplying \frac{9}{5} by the reciprocal of \frac{5}{2}.
\sqrt{\left(\frac{5}{9}\times \frac{18}{25}\right)^{2}}
Multiply \frac{9}{5} and \frac{2}{5} to get \frac{18}{25}.
\sqrt{\left(\frac{2}{5}\right)^{2}}
Multiply \frac{5}{9} and \frac{18}{25} to get \frac{2}{5}.
\sqrt{\frac{4}{25}}
Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.
\frac{2}{5}
Rewrite the square root of the division \frac{4}{25} as the division of square roots \frac{\sqrt{4}}{\sqrt{25}}. Take the square root of both numerator and denominator.