What is the value of `sqrt(361+sqrt(625)+sqrt196)`

Options

A. 21
B. 19
C. 20
D. 17

Answer

To solve the expression \( \sqrt{361 + \sqrt{625} + \sqrt{196}} \), we will follow these steps:

### Step 1: Calculate \( \sqrt{625} \)
The square root of 625 is:
\[ \sqrt{625} = 25 \]

### Step 2: Calculate \( \sqrt{196} \)
The square root of 196 is:
\[ \sqrt{196} = 14 \]

### Step 3: Substitute the values back into the expression
Now we substitute the values we found back into the expression:
\[ \sqrt{361 + \sqrt{625} + \sqrt{196}} = \sqrt{361 + 25 + 14} \]

### Step 4: Add the numbers inside the square root
Now, we add the numbers inside the square root:
\[ 361 + 25 + 14 = 400 \]

### Step 5: Calculate \( \sqrt{400} \)
Finally, we calculate the square root of 400:
\[ \sqrt{400} = 20 \]

### Final Answer
Thus, the value of \( \sqrt{361 + \sqrt{625} + \sqrt{196}} \) is:
\[ \boxed{20} \]