What approximate value will come in place of question mark (?) in the following questions. (You are not expected to calculate the exact value)
`(10.011)^(2) + (23.989)^(2) = 275.99 + (?)^(2)`

Options

A. 34
B. 6
C. 28
D. 20

Answer

To solve the equation \( (10.011)^{2} + (23.989)^{2} = 275.99 + (?)^{2} \) and find the approximate value for the question mark (?), we can follow these steps:

### Step 1: Round the numbers to the nearest integers
- Round \( 10.011 \) to \( 10 \)
- Round \( 23.989 \) to \( 24 \)
- Round \( 275.99 \) to \( 276 \)

### Step 2: Write the equation with the rounded values
Now we can rewrite the equation using these rounded values:
\[ (10)^{2} + (24)^{2} = 276 + (?)^{2} \]

### Step 3: Calculate the squares
Calculate the squares of the rounded numbers:
- \( (10)^{2} = 100 \)
- \( (24)^{2} = 576 \)

### Step 4: Substitute the squares back into the equation
Substituting these values into the equation gives:
\[ 100 + 576 = 276 + (?)^{2} \]

### Step 5: Simplify the equation
Combine the left side:
\[ 676 = 276 + (?)^{2} \]

### Step 6: Isolate the square term
To isolate \( (?)^{2} \), subtract \( 276 \) from both sides:
\[ 676 - 276 = (?)^{2} \]
\[ 400 = (?)^{2} \]

### Step 7: Take the square root
Now, take the square root of both sides to find \( ? \):
\[ ? = \sqrt{400} = 20 \]

Thus, the approximate value that will come in place of the question mark (?) is **20**.

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