Let's simplify the expression $3\sqrt{5}(4\sqrt{2})$.

1. Multiply the constants: $3 \times 4 = 12$.
2. Now, multiply the square roots: $\sqrt{5} \times \sqrt{2} = \sqrt{10}$.

So, the simplified expression is:

$12\sqrt{10}$

Would you like further details on this simplification or have any questions?

Here are five related questions for practice:

1. Simplify $2\sqrt{3} \times 5\sqrt{7}$.
2. Simplify $\sqrt{12} \times \sqrt{3}$.
3. Multiply $6\sqrt{2} \times 4\sqrt{5}$.
4. Simplify $7\sqrt{11} \times 3\sqrt{2}$.
5. Simplify $8\sqrt{6} \times 2\sqrt{3}$.

Tip: When multiplying square roots, remember $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$.