Square Root Quotient Property: Identify the greater value

To solve this problem, we will simplify each square root expression separately and compare them:

• Simplify $\sqrt{\frac{4}{2}}$:

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

• Simplify $\sqrt{\frac{6}{3}}$:

$\sqrt{\frac{6}{3}} = \sqrt{2}$

• Simplify $\sqrt{\frac{8}{4}}$:

$\sqrt{\frac{8}{4}} = \sqrt{2}$

Upon simplification, each expression results in $\sqrt{2}$. Therefore, all values are equal.

Thus, the correct choice is: All values are equal.

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 $\sqrt{\frac{36}{6}}$.

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

• Step 1: Simplify each choice using the Square Root Quotient Property.
• Step 2: Calculate the square root of each simplified fraction.
• Step 3: Compare these values to find the largest one.

Now, let's work through each step:

Step 1: Simplify each choice:
Choice 1: $\sqrt{\frac{36}{4}} = \frac{\sqrt{36}}{\sqrt{4}} = \frac{6}{2} = 3$
Choice 2: $\sqrt{\frac{36}{16}} = \frac{\sqrt{36}}{\sqrt{16}} = \frac{6}{4} = 1.5$
Choice 3: $\sqrt{\frac{36}{6}} = \frac{\sqrt{36}}{\sqrt{6}} = \frac{6}{\sqrt{6}} \approx 2.45$ (approximating since it is irrational)
Choice 4: $\sqrt{\frac{36}{2}} = \frac{\sqrt{36}}{\sqrt{2}} = \frac{6}{\sqrt{2}} = \frac{6 \times \sqrt{2}}{2} = 3\sqrt{2} \approx 4.24$

Step 2: Evaluate to find which is the largest value:
Choice 1 equals 3, Choice 2 equals 1.5, Choice 3 equals approximately 2.45, and Choice 4 approximately equals 4.24.

Step 3: Compare these values. Clearly, $4.24$ is the largest.

Therefore, the solution to the problem is $\sqrt{\frac{36}{2}}$.

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 $\sqrt{\frac{64}{8}}$.