Maximum Value Comparison: Identifying the Largest Number

To solve this problem, we'll follow these steps:

• Step 1: Simplify each expression using the Square Root Quotient Property.
• Step 2: Compare the simplified values to identify the largest one.

Let's simplify each expression:

Choice 1: $\sqrt{\frac{25}{5}}$
Simplify: $\sqrt{\frac{25}{5}} = \sqrt{5} \approx 2.236$ since $\frac{25}{5} = 5$.

Choice 2: $\sqrt{\frac{36}{6}}$
Simplify: $\sqrt{\frac{36}{6}} = \sqrt{6} \approx 2.449$ since $\frac{36}{6} = 6$.

Choice 3: $\sqrt{\frac{49}{7}}$
Simplify: $\sqrt{\frac{49}{7}} = \sqrt{7} \approx 2.646$ since $\frac{49}{7} = 7$.

Choice 4: $\sqrt{\frac{64}{8}}$
Simplify: $\sqrt{\frac{64}{8}} = \sqrt{8} \approx 2.828$ since $\frac{64}{8} = 8$.

Upon comparing the values, $\sqrt{8} \approx 2.828$ is the largest.

Therefore, the largest value is $\sqrt{\frac{64}{8}}$.