1. **Problem statement:** We are given two disks with areas 2.5 and 100, and we want to find the ratio of their radii. 2. **Formula used:** The area $A$ of a disk is related to its radius $r$ by the formula $$A = \pi r^2$$ 3. **Step 1:** Express the radii in terms of the areas: $$r = \sqrt{\frac{A}{\pi}}$$ 4. **Step 2:** Calculate the radius of the small disk: $$r_{small} = \sqrt{\frac{2.5}{\pi}}$$ 5. **Step 3:** Calculate the radius of the large disk: $$r_{large} = \sqrt{\frac{100}{\pi}}$$ 6. **Step 4:** Find the ratio of the radii: $$\frac{r_{large}}{r_{small}} = \frac{\sqrt{\frac{100}{\pi}}}{\sqrt{\frac{2.5}{\pi}}} = \sqrt{\frac{100}{2.5}} = \sqrt{40} = 2\sqrt{10} \approx 6.324$$ **Final answer:** The ratio of the radii of the large disk to the small disk is approximately $6.324$.