What is the value of `sqrt(1054+sqrt(196)+sqrt(169)+sqrt(64))`?

Options

A. 33
B. 37
C. 29
D. 31

Answer

To solve the expression \( \sqrt{1054 + \sqrt{196} + \sqrt{169} + \sqrt{64}} \), we will break it down step by step.

### Step 1: Calculate the square roots
First, we need to find the square roots of the numbers inside the expression:

1. \( \sqrt{196} = 14 \) (since \( 14 \times 14 = 196 \))
2. \( \sqrt{169} = 13 \) (since \( 13 \times 13 = 169 \))
3. \( \sqrt{64} = 8 \) (since \( 8 \times 8 = 64 \))

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

\[ \sqrt{1054 + 14 + 13 + 8} \]

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

\[ 1054 + 14 + 13 + 8 = 1054 + 35 = 1089 \]

### Step 4: Calculate the square root of the sum
Now we need to find the square root of 1089:

\[ \sqrt{1089} \]

### Step 5: Determine the square root
The square root of 1089 is 33 (since \( 33 \times 33 = 1089 \)).

### Final Answer
Thus, the value of \( \sqrt{1054 + \sqrt{196} + \sqrt{169} + \sqrt{64}} \) is:

\[ \boxed{33} \]

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