\[\sqrt{810} \cdot \sqrt{640} = \sqrt{810 \cdot 640} =\]
\[= \sqrt{81 \cdot 10 \cdot 64 \cdot 10} =\]
\[= \sqrt{81 \cdot 64 \cdot 100} =\]
\[= 9 \cdot 8 \cdot 10 = 720\]