1. **State the problem:** Simplify the expression $4\sqrt{112}$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. **Factor 112 into a product involving a perfect square:** $$112 = 16 \times 7$$ 4. **Rewrite the expression using this factorization:** $$4\sqrt{112} = 4\sqrt{16 \times 7}$$ 5. **Apply the square root product rule:** $$4\sqrt{16 \times 7} = 4 \times \sqrt{16} \times \sqrt{7}$$ 6. **Evaluate the square root of the perfect square:** $$\sqrt{16} = 4$$ 7. **Substitute back:** $$4 \times 4 \times \sqrt{7} = 16\sqrt{7}$$ 8. **Final answer:** $$4\sqrt{112} = 16\sqrt{7}$$