#### Answer

$35xy\sqrt {6x}$

#### Work Step by Step

Step 1: $5\sqrt {3xy}\times7x\sqrt {2y}$
Step 2: $5\times7x\times\sqrt {3xy}\times\sqrt {2y}$
Step 3: $35x\times\sqrt {3xy\times2y}$
Step 4: $35x\times\sqrt {6xy^{2}}$
Step 5: $35x\times\sqrt {y^{2}}\times\sqrt {6x}$
Step 6: $35xy\sqrt {6x}$