Question: Tom owns a square plot of land. He knows that the area of the plot is between 3000 and 3100 square meters.
1. **State the problem:**
Tom has a square plot of land with an area between $3000$ and $3100$ square meters. We want to find the possible range for the side length of the square.
2. **Formula used:**
The area $A$ of a square with side length $s$ is given by:
$$A = s^2$$
3. **Set up inequalities:**
Since the area is between $3000$ and $3100$, we write:
$$3000 < s^2 < 3100$$
4. **Solve for $s$ by taking square roots:**
$$\sqrt{3000} < s < \sqrt{3100}$$
5. **Calculate approximate values:**
$$\sqrt{3000} \approx 54.77$$
$$\sqrt{3100} \approx 55.68$$
6. **Interpretation:**
The side length $s$ of the square plot is between approximately $54.77$ meters and $55.68$ meters.
**Final answer:**
$$54.77 < s < 55.68$$