If `(sqrt(x))/(2)=2sqrt(2)`, what is the value of x?

Options

A. `4`
B. `16`
C. `16sqrt(2)`
D. `32`

Answer

To solve the equation \(\frac{\sqrt{x}}{2} = 2\sqrt{2}\), we will follow these steps:

### Step 1: Multiply both sides by 2
To eliminate the fraction, we multiply both sides of the equation by 2.

\[ \sqrt{x} = 2\sqrt{2} \times 2 \]

### Step 2: Simplify the right side
Now we simplify the right side:

\[ \sqrt{x} = 4\sqrt{2} \]

### Step 3: Square both sides
Next, we square both sides to solve for \(x\):

\[ x = (4\sqrt{2})^2 \]

### Step 4: Calculate the square
Now we calculate the square:

\[ x = 4^2 \times (\sqrt{2})^2 = 16 \times 2 \]

### Step 5: Final calculation
Now we multiply to find the value of \(x\):

\[ x = 32 \]

Thus, the value of \(x\) is \(32\).

### Summary of Steps:
1. Multiply both sides by 2.
2. Simplify the right side.
3. Square both sides.
4. Calculate the square.
5. Multiply to find the final value.