Ratio and Proportion

Concept:Compounded ratio is found by multiplying the two given ratios.Duplicate ratio squares each term of a ratio.Triplicate ratio cubes each term of a ratio.Explanation:Step 1: Find the duplicate ratio of $\sqrt{5}:\sqrt{6}$.Square both terms: $(\sqrt{5})^2 : (\sqrt{6})^2 = 5 : 6$.Step 2: Find the triplicate ratio of $3:5$.Cube both terms: $3^3 : 5^3 = 27 : 125$.Step 3: Compute the compounded ratio.Multiply the two ratios: $\frac{5}{6} \times \frac{27}{125} = \frac{135}{750}$.Simplify: $\frac{135}{750} = \frac{9}{50}$.Thus, the compounded ratio is $9:50$.Answer:$9:50$