Ratio and Proportion

Concept:We substitute the given ratio into the expression and simplify using basic algebra.Explanation:The ratio $a:b = 4:1$ means $a$ is 4 times $b$.Let $a = 4k$ and $b = k$ for some positive constant $k$.Now compute each square root separately.First, $\sqrt{\frac{a}{b}} = \sqrt{\frac{4k}{k}} = \sqrt{4} = 2$.Second, $\sqrt{\frac{b}{a}} = \sqrt{\frac{k}{4k}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Add them together: $2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}$.Check the given options: A. $1$, B. $\frac{5}{4}$, C. $\frac{4}{5}$, D. None.Since $\frac{5}{2}$ is not equal to any of the first three options, the correct choice is "None".Answer:D. None