1. **State the problem:** We need to find three numbers that lie between $\frac{\pi}{2}$ and $\sqrt{48}$ on the number line. 2. **Calculate the approximate values:** - $\frac{\pi}{2} \approx \frac{3.1416}{2} = 1.5708$ - $\sqrt{48} = \sqrt{16 \times 3} = 4 \sqrt{3} \approx 4 \times 1.732 = 6.928$ 3. **Interpretation:** We are looking for numbers between approximately $1.5708$ and $6.928$. 4. **Select numbers:** Any numbers greater than $1.5708$ and less than $6.928$ are between these two points. 5. **Example numbers between:** - $2$ - $3$ - $5$ These three numbers are all between $\frac{\pi}{2}$ and $\sqrt{48}$ on the number line. **Final answer:** The numbers $2$, $3$, and $5$ are located between $\frac{\pi}{2}$ and $\sqrt{48}$ on the number line.