1. **State the problem:** Simplify the expression $\sqrt{16} + 12\sqrt{55}$.\n\n2. **Recall the square root properties:** The square root of a product can be written as the product of square roots: $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$. Also, $\sqrt{16}$ is a perfect square.\n\n3. **Simplify $\sqrt{16}$:** Since $16 = 4^2$, $\sqrt{16} = 4$.\n\n4. **Rewrite the expression:** The expression becomes $4 + 12\sqrt{55}$.\n\n5. **Check if $\sqrt{55}$ can be simplified:** $55 = 5 \times 11$, both prime, so $\sqrt{55}$ cannot be simplified further.\n\n6. **Final simplified form:** $4 + 12\sqrt{55}$. This is the simplest form since the terms are unlike radicals and cannot be combined further.