The value of `(10 sqrt(6.25))/(sqrt(6.25) - 0.5)` is:

Options

A. 125
B. `0.125`
C. `1.25`
D. `12.5`

Answer

To solve the expression \((10 \sqrt{6.25}) / (\sqrt{6.25} - 0.5)\), we will follow these steps:

### Step 1: Calculate \(\sqrt{6.25}\)
First, we need to find the square root of \(6.25\).

\[ \sqrt{6.25} = 2.5 \]

### Step 2: Substitute \(\sqrt{6.25}\) back into the expression
Now, we substitute \(2.5\) back into the original expression:

\[ \frac{10 \cdot 2.5}{2.5 - 0.5} \]

### Step 3: Simplify the denominator
Next, we simplify the denominator:

\[ 2.5 - 0.5 = 2.0 \]

### Step 4: Substitute the simplified denominator
Now, we substitute this back into the expression:

\[ \frac{10 \cdot 2.5}{2.0} \]

### Step 5: Calculate the numerator
Now, we calculate the numerator:

\[ 10 \cdot 2.5 = 25 \]

### Step 6: Final calculation
Now we can perform the final calculation:

\[ \frac{25}{2.0} = 12.5 \]

Thus, the value of \(\frac{10 \sqrt{6.25}}{\sqrt{6.25} - 0.5}\) is \(12.5\).

### Final Answer:
\[ \text{The value is } 12.5 \]

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