Simplify $\sqrt{15}\cdot\sqrt{35}$.
I notice that both 15 and 35 have a common factor of 5, so I can use the property that $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ to rewrite the expression as $\sqrt{5}\cdot\sqrt{3}\cdot\sqrt{5}\cdot\sqrt{7}$. Now I can pair up the two $\sqrt{5}$ terms and use the property that $\sqrt{a}\cdot\sqrt{a}=a$ to simplify them as $5\cdot\sqrt{3}\cdot\sqrt{7}$. 