If `(sqrt(a) + sqrt(b)) = 17 and (sqrt(a) - sqrt(b)) = 1`, then the value of `sqrt(ab)` is :

Options

A. 72
B. 27
C. 35
D. none of these

Answer

To solve the problem step by step, we start with the given equations:

1. \( \sqrt{a} + \sqrt{b} = 17 \) (Equation 1)
2. \( \sqrt{a} - \sqrt{b} = 1 \) (Equation 2)

### Step 1: Assign Variables
Let \( \sqrt{a} = x \) and \( \sqrt{b} = y \). Thus, we can rewrite the equations as:
- \( x + y = 17 \) (Equation 1)
- \( x - y = 1 \) (Equation 2)

### Step 2: Add the Equations
Now, we will add Equation 1 and Equation 2:
\[ (x + y) + (x - y) = 17 + 1 \]
This simplifies to:
\[ 2x = 18 \]

### Step 3: Solve for \( x \)
Now, divide both sides by 2:
\[ x = \frac{18}{2} = 9 \]

### Step 4: Substitute \( x \) back to find \( y \)
Now that we have \( x \), we can substitute it back into Equation 1 to find \( y \):
\[ 9 + y = 17 \]
Subtract 9 from both sides:
\[ y = 17 - 9 = 8 \]

### Step 5: Find \( \sqrt{ab} \)
Now, we know \( \sqrt{a} = x = 9 \) and \( \sqrt{b} = y = 8 \). We need to find \( \sqrt{ab} \):
\[ \sqrt{ab} = \sqrt{a} \cdot \sqrt{b} = x \cdot y = 9 \cdot 8 \]
Calculating this gives:
\[ \sqrt{ab} = 72 \]

### Final Answer
Thus, the value of \( \sqrt{ab} \) is **72**.

---