1. **State the problem:** Simplify the expression $$16) \frac{\sqrt{972}}{\sqrt{4}}$$. 2. **Recall the property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$. 3. **Apply the property:** $$\frac{\sqrt{972}}{\sqrt{4}} = \sqrt{\frac{972}{4}}$$ 4. **Simplify the fraction inside the square root:** $$\frac{972}{4} = 243$$ 5. **Rewrite the expression:** $$16) \sqrt{243}$$ 6. **Simplify $$\sqrt{243}$$ by prime factorization:** $$243 = 3^5 = 3^4 \times 3 = (3^2)^2 \times 3 = 9^2 \times 3$$ 7. **Use the property $$\sqrt{a^2 \times b} = a \sqrt{b}$$:** $$\sqrt{243} = \sqrt{9^2 \times 3} = 9 \sqrt{3}$$ 8. **Final simplified expression:** $$16) \times 9 \sqrt{3} = 144 \sqrt{3}$$ **Answer:** $$144 \sqrt{3}$$