1. **State the problem:** Simplify the expression $\sqrt{16} + \sqrt{192}$ and express it in the form $\sqrt{a} + b$. Then find the value of $a - b$. 2. **Simplify each square root:** - $\sqrt{16} = 4$ because $4^2 = 16$. - For $\sqrt{192}$, factor 192 into perfect squares: $192 = 64 \times 3$. 3. **Simplify $\sqrt{192}$:** $$\sqrt{192} = \sqrt{64 \times 3} = \sqrt{64} \times \sqrt{3} = 8\sqrt{3}$$ 4. **Rewrite the original expression:** $$\sqrt{16} + \sqrt{192} = 4 + 8\sqrt{3}$$ 5. **Express in the form $\sqrt{a} + b$:** Here, $b = 4$ and $\sqrt{a} = 8\sqrt{3}$. 6. **Find $a$:** Since $8\sqrt{3} = \sqrt{a}$, square both sides: $$\left(8\sqrt{3}\right)^2 = a$$ $$64 \times 3 = a$$ $$a = 192$$ 7. **Calculate $a - b$:** $$a - b = 192 - 4 = 188$$ **Final answer:** $188$