What value will come in place of question mark (?) in the following question ?
`sqrt((?)/(196))=(32)/(56)`

Options

A. 84
B. 64
C. 74
D. 94

Answer

To solve the equation \( \sqrt{\frac{?}{196}} = \frac{32}{56} \), we will follow these steps:

### Step 1: Rewrite the equation
Let \( x \) be the value that replaces the question mark. The equation can be rewritten as:
\[ \sqrt{\frac{x}{196}} = \frac{32}{56} \]

### Step 2: Simplify the right side
We can simplify \( \frac{32}{56} \):
\[ \frac{32}{56} = \frac{32 \div 8}{56 \div 8} = \frac{4}{7} \]
So now the equation is:
\[ \sqrt{\frac{x}{196}} = \frac{4}{7} \]

### Step 3: Square both sides
To eliminate the square root, we square both sides of the equation:
\[ \left(\sqrt{\frac{x}{196}}\right)^2 = \left(\frac{4}{7}\right)^2 \]
This simplifies to:
\[ \frac{x}{196} = \frac{16}{49} \]

### Step 4: Cross-multiply
Now, we can cross-multiply to solve for \( x \):
\[ x \cdot 49 = 16 \cdot 196 \]
Calculating \( 16 \cdot 196 \):
\[ 16 \cdot 196 = 3136 \]
Thus, we have:
\[ 49x = 3136 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 49:
\[ x = \frac{3136}{49} \]
Calculating \( \frac{3136}{49} \):
\[ x = 64 \]

### Final Answer
The value that will come in place of the question mark is:
\[ \boxed{64} \]