$\displaystyle { \frac{(5\sqrt6)^2}{10}=\frac {5^2 \cdot (\sqrt6)^2}{10}= \frac {25 \cdot6}{10} }$   

 $\displaystyle { \frac {5 \cdot5 \cdot 3 \cdot 2}{5 \cdot 2} = \frac {5 \cdot 3}{ 1} =15 }$