What is the value of x if `sqrt((x)/(7))=2.74` ?

Options

A. `52.55`
B. `57.54`
C. `94.87`
D. `105.11`

Explanation

To solve the equation \( \sqrt{\frac{x}{7}} = 2.74 \), we will follow these steps:

### Step 1: Square both sides
To eliminate the square root, we square both sides of the equation:

\[ \left(\sqrt{\frac{x}{7}}\right)^2 = (2.74)^2 \]

### Step 2: Simplify the left side
The left side simplifies to:

\[ \frac{x}{7} = (2.74)^2 \]

### Step 3: Calculate \( (2.74)^2 \)
Now we calculate \( (2.74)^2 \):

\[ (2.74)^2 = 7.5076 \]

### Step 4: Set up the equation
Now we have:

\[ \frac{x}{7} = 7.5076 \]

### Step 5: Multiply both sides by 7
To solve for \( x \), we multiply both sides by 7:

\[ x = 7 \times 7.5076 \]

### Step 6: Calculate \( x \)
Now we perform the multiplication:

\[ x = 52.5532 \]

### Step 7: Round if necessary
Since the options provided are rounded, we can round \( 52.5532 \) to \( 52.55 \).

Thus, the value of \( x \) is:

\[ \boxed{52.55} \]