What approximate value should come in place of question mark(?) in the following questions?
`sqrt((15.88xx7+52.05+13xx7.01))=?`

Options

A. 40
B. 32
C. 24
D. 16

Answer

To solve the expression \( \sqrt{(15.88 \times 7 + 52.05 + 13 \times 7.01)} \), we will follow these steps:

### Step 1: Approximate the values
We will round the numbers to make calculations easier:
- \( 15.88 \approx 16 \)
- \( 52.05 \approx 52 \)
- \( 7.01 \approx 7 \)

### Step 2: Substitute the approximated values into the expression
Now, we substitute these approximated values into the expression:
\[ \sqrt{(16 \times 7 + 52 + 13 \times 7)} \]

### Step 3: Calculate the multiplications
Next, we perform the multiplications:
- \( 16 \times 7 = 112 \)
- \( 13 \times 7 = 91 \)

### Step 4: Add the results
Now, we add these results along with 52:
\[ 112 + 52 + 91 \]

### Step 5: Perform the addition
Calculating the sum:
\[ 112 + 52 = 164 \]
\[ 164 + 91 = 255 \]

### Step 6: Take the square root
Now, we take the square root of the total:
\[ \sqrt{255} \]

### Step 7: Approximate the square root
To find the approximate value of \( \sqrt{255} \), we can estimate:
- \( \sqrt{256} = 16 \)
- Since \( 255 \) is slightly less than \( 256 \), \( \sqrt{255} \) will be slightly less than \( 16 \).

Thus, we can conclude that the approximate value that comes in place of the question mark is:
\[ \approx 16 \]

### Final Answer:
The approximate value is \( 16 \).

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