Mathematical Reasoning: Finding the Largest Value in a Set

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

• Step 1: Calculate the value of each expression under the square root.
• Step 2: Simplify the square roots to find their numerical values.
• Step 3: Compare the results to find the largest value.

Now, let's work through each step:

Step 1: Calculate the values under each square root.

• For choice 1: $\frac{25}{5} = 5$
• For choice 2: $\frac{36}{6} = 6$
• For choice 3: $\frac{36}{9} = 4$
• For choice 4: $\frac{8}{4} = 2$

Step 2: Compute the square roots.

• Choice 1: $\sqrt{5} \approx 2.236$
• Choice 2: $\sqrt{6} \approx 2.449$
• Choice 3: $\sqrt{4} = 2$
• Choice 4: $\sqrt{2} \approx 1.414$

Step 3: Compare the square roots calculated.

The largest value among the choices is found in choice 2:

$\sqrt{\frac{36}{6}} = \sqrt{6} \approx 2.449$ is larger than the other evaluated square roots.

Therefore, the largest value is given by the expression $\sqrt{\frac{36}{6}}$.