1. **State the problem:** We need to find which three numbers 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. **Evaluate the given numbers:** - $\frac{9}{4} = 2.25$ - $\sqrt{25} = 5$ - $3\pi = 3 \times 3.1416 = 9.4248$ - $2\pi = 2 \times 3.1416 = 6.2832$ - $\frac{3}{2} = 1.5$ 4. **Check which numbers lie between $1.5708$ and $6.928$:** - $\frac{9}{4} = 2.25$ (between) - $\sqrt{25} = 5$ (between) - $3\pi = 9.4248$ (not between) - $2\pi = 6.2832$ (between) - $\frac{3}{2} = 1.5$ (less than $1.5708$, so not between) 5. **Final answer:** The three numbers between $\frac{\pi}{2}$ and $\sqrt{48}$ are $\frac{9}{4}$, $\sqrt{25}$, and $2\pi$.