1. The problem asks to approximate $\pi + \sqrt{50}$ to the nearest hundredth. 2. Recall that $\pi \approx 3.14159$ and $\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}$. Since $\sqrt{2} \approx 1.414$, then $\sqrt{50} \approx 5 \times 1.414 = 7.07$. 3. Now add the approximations: $$\pi + \sqrt{50} \approx 3.14159 + 7.07 = 10.21159$$ 4. To round to the nearest hundredth, look at the third decimal place (1). Since it is less than 5, round down: $$10.21159 \approx 10.21$$ 5. Therefore, the approximate value of $\pi + \sqrt{50}$ to the nearest hundredth is **10.21**. Final answer: 10.21