What is the value of `sqrt(247+sqrt(81))` ?

Options

A. 14
B. 16
C. 18
D. 15

Answer

To solve the expression \( \sqrt{247 + \sqrt{81}} \), we can follow these steps:

### Step 1: Simplify \( \sqrt{81} \)
We know that \( \sqrt{81} = 9 \) because \( 9 \times 9 = 81 \).

### Step 2: Substitute back into the expression
Now we substitute \( \sqrt{81} \) back into the expression:
\[ \sqrt{247 + 9} \]

### Step 3: Add the numbers inside the square root
Next, we add \( 247 \) and \( 9 \):
\[ 247 + 9 = 256 \]

### Step 4: Take the square root of the sum
Now we take the square root of \( 256 \):
\[ \sqrt{256} = 16 \]
because \( 16 \times 16 = 256 \).

### Final Answer
Thus, the value of \( \sqrt{247 + \sqrt{81}} \) is:
\[ \boxed{16} \]