What approximate value will come in place of question mark (?) in the given question ? (You are not expected to calculate the exact value.)
`(sqrt(24.01xx2)+252.16)xx2=?`

Options

A. 462
B. 520
C. 412
D. 620

Answer

To solve the problem step by step, we will approximate the expression given in the question:

**Question:**
\[ (\sqrt{24.01 \times 2} + 252.16) \times 2 = ? \]

### Step 1: Approximate the square root term
We start with the term inside the square root:
\[ \sqrt{24.01 \times 2} \]
Since \(24.01\) is very close to \(24\), we can approximate it as:
\[ \sqrt{24 \times 2} \]
Calculating \(24 \times 2\):
\[ 24 \times 2 = 48 \]
Now we find the square root:
\[ \sqrt{48} \]

### Step 2: Simplify the square root
We can simplify \(\sqrt{48}\) as follows:
\[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]

### Step 3: Approximate \(\sqrt{3}\)
The approximate value of \(\sqrt{3}\) is about \(1.732\). However, for simplicity, we can round it to \(2\) since we are looking for an approximate value:
\[ 4\sqrt{3} \approx 4 \times 2 = 8 \]

### Step 4: Approximate the second term
Now we look at the second term in the expression:
\[ 252.16 \]
We can approximate this as:
\[ 252 \]
since \(0.16\) is less than \(0.5\).

### Step 5: Combine the approximated terms
Now we combine the approximated terms:
\[ \sqrt{24.01 \times 2} + 252 \approx 8 + 252 = 260 \]

### Step 6: Multiply by 2
Finally, we multiply the result by \(2\):
\[ 260 \times 2 = 520 \]

Thus, the approximate value that will come in place of the question mark (?) is:
\[ \boxed{520} \]