1. **State the problem:** Andrew bought a square piece of curtain material with an area of $5\frac{1}{16}$ meters squared. We need to find the length of one side of the square. 2. **Formula used:** For a square, the area $A$ is related to the side length $s$ by the formula: $$A = s^2$$ 3. **Convert the mixed fraction to an improper fraction:** $$5\frac{1}{16} = \frac{5 \times 16 + 1}{16} = \frac{80 + 1}{16} = \frac{81}{16}$$ 4. **Set up the equation:** $$s^2 = \frac{81}{16}$$ 5. **Solve for $s$ by taking the square root of both sides:** $$s = \sqrt{\frac{81}{16}}$$ 6. **Simplify the square root:** $$s = \frac{\sqrt{81}}{\sqrt{16}} = \frac{9}{4}$$ 7. **Convert to decimal or mixed number if desired:** $$\frac{9}{4} = 2\frac{1}{4} = 2.25$$ **Final answer:** The length of one side of the square curtain material is $\frac{9}{4}$ meters or 2.25 meters.