1. The problem asks to simplify $\sqrt{32}$ and enter the simplified numerical coefficient only. 2. Recall the property of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. 3. Factor 32 into a product of a perfect square and another number: $32 = 16 \times 2$. 4. Apply the square root property: $$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2}$$ 5. Since $\sqrt{16} = 4$, we have: $$\sqrt{32} = 4 \times \sqrt{2}$$ 6. The simplified numerical coefficient is therefore $4$. Final answer: 4