`(441)/(?)=(?)/(3364)`

Options

A. 1218
B. 1456
C. 2457
D. 6546

Explanation

To solve the equation \(\frac{441}{?} = \frac{?}{3364}\), we can follow these steps:

### Step 1: Set up the equation
Let’s denote the question mark as \(x\). Therefore, we can rewrite the equation as:
\[ \frac{441}{x} = \frac{x}{3364} \]

### Step 2: Cross-multiply
To eliminate the fractions, we can cross-multiply:
\[ 441 \cdot 3364 = x \cdot x \]
This simplifies to:
\[ 441 \cdot 3364 = x^2 \]

### Step 3: Calculate the product
Now, we need to calculate \(441 \cdot 3364\). We can simplify this by finding the square root of both sides later, but let's first compute the product:
\[ x^2 = 441 \cdot 3364 \]

### Step 4: Find the square root
Next, we take the square root of both sides to solve for \(x\):
\[ x = \sqrt{441 \cdot 3364} \]

### Step 5: Simplify the square root
We can break this down further:
\[ x = \sqrt{441} \cdot \sqrt{3364} \]
Calculating the square roots:
\[ \sqrt{441} = 21 \quad \text{and} \quad \sqrt{3364} = 58 \]
Thus, we have:
\[ x = 21 \cdot 58 \]

### Step 6: Multiply to find \(x\)
Now, we multiply \(21\) and \(58\):
\[ x = 1218 \]

### Final Answer
Therefore, the value of the question mark is:
\[ \boxed{1218} \]