`sqrt(?)+(3)/(5)` of `80=60xx(1)/(2)xx8`

Options

A. 38864
B. 46864
C. 56864
D. 66864

Answer

To solve the equation \( \sqrt{?} + \frac{3}{5} \cdot 80 = 60 \cdot \frac{1}{2} \cdot 8 \), we will follow these steps:

### Step 1: Simplify the right-hand side
First, we need to simplify the right-hand side of the equation:

\[ 60 \cdot \frac{1}{2} \cdot 8 \]

Calculating \( \frac{1}{2} \cdot 8 \):

\[ \frac{1}{2} \cdot 8 = 4 \]

Now multiply by 60:

\[ 60 \cdot 4 = 240 \]

So, the right-hand side simplifies to 240.

### Step 2: Simplify the left-hand side
Next, we simplify the left-hand side:

\[ \sqrt{?} + \frac{3}{5} \cdot 80 \]

Calculating \( \frac{3}{5} \cdot 80 \):

\[ \frac{3 \cdot 80}{5} = \frac{240}{5} = 48 \]

So, the left-hand side becomes:

\[ \sqrt{?} + 48 \]

### Step 3: Set up the equation
Now we set the left-hand side equal to the right-hand side:

\[ \sqrt{?} + 48 = 240 \]

### Step 4: Isolate the square root
To isolate \( \sqrt{?} \), we subtract 48 from both sides:

\[ \sqrt{?} = 240 - 48 \]

Calculating the right-hand side:

\[ \sqrt{?} = 192 \]

### Step 5: Square both sides
Now we square both sides to eliminate the square root:

\[ ? = 192^2 \]

Calculating \( 192^2 \):

\[ 192 \times 192 = 36864 \]

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

\[ ? = 36864 \]

---