What is the value of `sqrt(231+sqrt(81)+sqrt(256))`?

Options

A. 12
B. 14
C. 15
D. 16

Answer

To solve the expression \( \sqrt{231 + \sqrt{81} + \sqrt{256}} \), we can follow these steps:

### Step 1: Calculate the square roots
First, we need to find the values of \( \sqrt{81} \) and \( \sqrt{256} \).

- \( \sqrt{81} = 9 \)
- \( \sqrt{256} = 16 \)

### Step 2: Substitute the square roots back into the expression
Now, we can substitute these values back into the original expression:

\[ \sqrt{231 + \sqrt{81} + \sqrt{256}} = \sqrt{231 + 9 + 16} \]

### Step 3: Add the numbers inside the square root
Next, we add the numbers inside the square root:

\[ 231 + 9 + 16 = 231 + 25 = 256 \]

### Step 4: Calculate the square root of the sum
Now, we take the square root of the sum:

\[ \sqrt{256} = 16 \]

### Final Answer
Thus, the value of \( \sqrt{231 + \sqrt{81} + \sqrt{256}} \) is \( 16 \).

---