1. The problem is to simplify the expression $3\sqrt{282}$. 2. Recall that the square root of a product can be written as the product of the square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$ 3. We want to factor 282 to find any perfect squares: $$282 = 2 \times 3 \times 47$$ 4. None of these factors are perfect squares, so $\sqrt{282}$ cannot be simplified further. 5. Therefore, the expression remains: $$3\sqrt{282}$$ 6. This is the simplest form since 282 has no perfect square factors other than 1.