`sqrt(?/(289))=54/51`

Options

A. 108
B. 324
C. 2916
D. 6800

Answer

To solve the equation \( \sqrt{\frac{?}{289}} = \frac{54}{51} \), we will follow these steps:

### Step 1: Square both sides of the equation
We start by squaring both sides to eliminate the square root.

\[ \left(\sqrt{\frac{?}{289}}\right)^2 = \left(\frac{54}{51}\right)^2 \]

This simplifies to:

\[ \frac{?}{289} = \frac{54^2}{51^2} \]

### Step 2: Calculate \(54^2\) and \(51^2\)
Now we calculate \(54^2\) and \(51^2\):

\[ 54^2 = 2916 \]
\[ 51^2 = 2601 \]

### Step 3: Substitute the squares back into the equation
Substituting these values back into the equation gives us:

\[ \frac{?}{289} = \frac{2916}{2601} \]

### Step 4: Cross-multiply to solve for ?
Cross-multiplying gives:

\[ ? \cdot 2601 = 2916 \cdot 289 \]

### Step 5: Calculate \(2916 \cdot 289\)
Now we calculate \(2916 \cdot 289\):

\[ 2916 \cdot 289 = 841944 \]

### Step 6: Solve for ?
Now we can solve for \(?\):

\[ ? = \frac{841944}{2601} \]

### Step 7: Perform the division
Now we perform the division:

\[ ? = 324 \]

### Final Answer
Thus, the value of the question mark is:

\[ ? = 324 \]