1. The problem is to simplify the expression $(5\sqrt{3})(3\sqrt{6})$. 2. Recall the multiplication rule for radicals: $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$. 3. Multiply the coefficients (numbers outside the radicals): $5 \times 3 = 15$. 4. Multiply the radicands (numbers inside the radicals): $\sqrt{3} \times \sqrt{6} = \sqrt{3 \times 6} = \sqrt{18}$. 5. So the expression becomes $15 \sqrt{18}$. 6. Simplify $\sqrt{18}$ by factoring 18 into $9 \times 2$, so $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3 \sqrt{2}$. 7. Substitute back: $15 \sqrt{18} = 15 \times 3 \sqrt{2} = 45 \sqrt{2}$. 8. Therefore, the simplified form is $45 \sqrt{2}$. Final answer: D. $45 \sqrt{2}$