Solve: Adding Square Roots of Fractions 49/4 and 9/36

To solve this problem, we'll proceed with the following steps:

• Step 1: Simplify $\sqrt{\frac{49}{4}}$.
• Step 2: Simplify $\sqrt{\frac{9}{36}}$.
• Step 3: Add the results obtained from Step 1 and Step 2.

Step 1: We use the square root of a quotient property $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$. For $\sqrt{\frac{49}{4}}$:

$\sqrt{\frac{49}{4}} = \frac{\sqrt{49}}{\sqrt{4}} = \frac{7}{2}$

Step 2: Similarly, apply the same property to $\sqrt{\frac{9}{36}}$:

$\sqrt{\frac{9}{36}} = \frac{\sqrt{9}}{\sqrt{36}} = \frac{3}{6} = \frac{1}{2}$

Step 3: Add the two results obtained:

$\frac{7}{2} + \frac{1}{2} = \frac{7 + 1}{2} = \frac{8}{2} = 4$

Therefore, the solution to the problem is $4$.