`(sqrt(4356)xxsqrt(?))/(sqrt(6084))=11`

Options

A. 144
B. 196
C. 169
D. 81

Explanation

To solve the equation \((\sqrt{4356} \times \sqrt{?}) / \sqrt{6084} = 11\), we will follow these steps:

### Step 1: Simplify the square roots
First, we need to find the square roots of the numbers involved.

- \(\sqrt{4356} = 66\) (since \(66 \times 66 = 4356\))
- \(\sqrt{6084} = 78\) (since \(78 \times 78 = 6084\))

Now, we can rewrite the equation as:
\[ \frac{66 \times \sqrt{?}}{78} = 11 \]

### Step 2: Cross-multiply to eliminate the fraction
To eliminate the fraction, we can cross-multiply:
\[ 66 \times \sqrt{?} = 11 \times 78 \]

### Step 3: Calculate \(11 \times 78\)
Now, calculate \(11 \times 78\):
\[ 11 \times 78 = 858 \]

So, we have:
\[ 66 \times \sqrt{?} = 858 \]

### Step 4: Isolate \(\sqrt{?}\)
Next, we isolate \(\sqrt{?}\) by dividing both sides by 66:
\[ \sqrt{?} = \frac{858}{66} \]

### Step 5: Simplify \(\frac{858}{66}\)
Now, we simplify \(\frac{858}{66}\):
\[ \frac{858}{66} = 13 \]

### Step 6: Solve for ?
Now, we square both sides to solve for \(?\):
\[ ? = 13^2 = 169 \]

### Final Answer
Thus, the value of the question mark is:
\[ \boxed{169} \]

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