1. **State the problem:** Simplify the expression $\sqrt{3a} \times \sqrt{6a}$.\n\n2. **Recall the property of square roots:** The product of square roots is the square root of the product, i.e., $\sqrt{x} \times \sqrt{y} = \sqrt{xy}$.\n\n3. **Apply the property:** $$\sqrt{3a} \times \sqrt{6a} = \sqrt{3a \times 6a}$$\n\n4. **Multiply inside the square root:** $$\sqrt{3a \times 6a} = \sqrt{18a^2}$$\n\n5. **Simplify the square root:** $$\sqrt{18a^2} = \sqrt{9 \times 2 \times a^2}$$\n\n6. **Use the rule $\sqrt{xy} = \sqrt{x} \times \sqrt{y}$:** $$\sqrt{9 \times 2 \times a^2} = \sqrt{9} \times \sqrt{2} \times \sqrt{a^2}$$\n\n7. **Evaluate the square roots of perfect squares:** $$\sqrt{9} = 3, \quad \sqrt{a^2} = a$$\n\n8. **Combine the results:** $$3 \times \sqrt{2} \times a = 3a\sqrt{2}$$\n\n**Final answer:** $3a\sqrt{2}$