1. **State the problem:** Chu needs carpet for a square room with an area of 15 m². The carpet rolls are 3.8 m wide. We need to determine if the carpet can cover the room without seams. 2. **Find the side length of the square room:** Since the room is square, the side length $s$ satisfies $$s^2 = 15$$ Taking the square root, $$s = \sqrt{15}$$ 3. **Calculate the numerical value:** $$s \approx 3.873$$ meters 4. **Compare the side length with the carpet roll width:** The carpet roll width is 3.8 m, which is less than the side length 3.873 m. 5. **Conclusion:** Since the carpet roll width (3.8 m) is less than the side length of the room (3.873 m), the carpet cannot cover the room in one piece without seams. **Final answer:** No, the store will not be able to install the carpet without a seam because the roll width is smaller than the room's side length.