What approximate value in come in place of question mark (?) in the given question ? (You are not expected to calculate the exact value.)
`319div8.02+ sqrt82 +?=(8.023)^2`

Options

A. 15
B. 36
C. 8
D. 26

Answer

To solve the equation \( 319 \div 8.02 + \sqrt{82} + ? = (8.023)^2 \), we will approximate each term step by step.

### Step 1: Approximate \( 319 \div 8.02 \)

Since \( 8.02 \) is very close to \( 8 \), we can approximate:

\[ 319 \div 8.02 \approx 319 \div 8 \]

Calculating \( 319 \div 8 \):

\[ 319 \div 8 = 39.875 \approx 40 \]

### Step 2: Approximate \( \sqrt{82} \)

We know that \( \sqrt{81} = 9 \) and \( \sqrt{100} = 10 \). Since \( 82 \) is close to \( 81 \), we can approximate:

\[ \sqrt{82} \approx 9 \]

### Step 3: Approximate \( (8.023)^2 \)

Since \( 8.023 \) is very close to \( 8 \), we can approximate:

\[ (8.023)^2 \approx 8^2 = 64 \]

### Step 4: Substitute the approximations into the equation

Now substituting our approximations into the equation:

\[ 40 + 9 + ? = 64 \]

### Step 5: Solve for \( ? \)

Now, we can simplify the equation:

\[ 49 + ? = 64 \]

To find \( ? \), we subtract \( 49 \) from \( 64 \):

\[ ? = 64 - 49 = 15 \]

### Final Answer

The approximate value of \( ? \) is \( 15 \).

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