What is the value of `sqrt(269-sqrt169)`?

Options

A. a)17
B. b)15
C. c)22
D. d)16

Answer

To find the value of \( \sqrt{269 - \sqrt{169}} \), we can follow these steps:

### Step 1: Calculate \( \sqrt{169} \)
First, we need to find the square root of 169.
\[ \sqrt{169} = 13 \]

### Step 2: Substitute \( \sqrt{169} \) into the expression
Now, we substitute \( \sqrt{169} \) back into the original expression:
\[ \sqrt{269 - \sqrt{169}} = \sqrt{269 - 13} \]

### Step 3: Perform the subtraction
Next, we perform the subtraction inside the square root:
\[ 269 - 13 = 256 \]

### Step 4: Calculate \( \sqrt{256} \)
Now, we need to find the square root of 256:
\[ \sqrt{256} = 16 \]

### Final Answer
Thus, the value of \( \sqrt{269 - \sqrt{169}} \) is:
\[ \boxed{16} \]

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