What is the value of `sqrt(256+sqrt(484)+sqrt(121))` ?

Options

A. 16
B. 18
C. 17
D. 19

Answer

To solve the expression \( \sqrt{256 + \sqrt{484} + \sqrt{121}} \), we will break it down step by step.

### Step 1: Calculate \( \sqrt{484} \)
- The square root of 484 can be calculated as follows:
\[ \sqrt{484} = 22 \]

### Step 2: Calculate \( \sqrt{121} \)
- The square root of 121 can be calculated as follows:
\[ \sqrt{121} = 11 \]

### Step 3: Substitute the values back into the expression
- Now we substitute the values we found into the original expression:
\[ \sqrt{256 + \sqrt{484} + \sqrt{121}} = \sqrt{256 + 22 + 11} \]

### Step 4: Simplify the expression inside the square root
- Now we add the numbers inside the square root:
\[ 256 + 22 + 11 = 289 \]

### Step 5: Calculate the square root of the sum
- Finally, we calculate the square root of 289:
\[ \sqrt{289} = 17 \]

### Final Answer
Thus, the value of \( \sqrt{256 + \sqrt{484} + \sqrt{121}} \) is \( 17 \).

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