`sqrt(4375)/sqrt(7)`=?

Options

A. 24.75
B. 27.25
C. 25
D. 35

Answer

To solve the expression \(\frac{\sqrt{4375}}{\sqrt{7}}\), we can follow these steps:

### Step 1: Combine the square roots
Using the property of square roots that states \(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\), we can rewrite the expression:
\[ \frac{\sqrt{4375}}{\sqrt{7}} = \sqrt{\frac{4375}{7}} \]

### Step 2: Calculate \(4375 \div 7\)
Now we need to perform the division:
\[ 4375 \div 7 = 625 \]

### Step 3: Substitute back into the square root
Now we can substitute this result back into the square root:
\[ \sqrt{\frac{4375}{7}} = \sqrt{625} \]

### Step 4: Calculate the square root of 625
Next, we find the square root of 625:
\[ \sqrt{625} = 25 \]

### Final Answer
Thus, the final answer is:
\[ \frac{\sqrt{4375}}{\sqrt{7}} = 25 \]