What approximate value will come in place of question mark (?) in the following questions. (You are not expected to calculate the exact value)
`(42.02)^(2) + (6.98)^(2) - (27.02)^(2) = (33.01)^(2) - ?`

Options

A. 1
B. 2
C. 3
D. 5

Answer

To find the approximate value that will come in place of the question mark (?) in the equation

\[ (42.02)^2 + (6.98)^2 - (27.02)^2 = (33.01)^2 - ? \]

we can follow these steps:

### Step 1: Approximate the numbers
First, we can round the numbers to make the calculations simpler.

- \(42.02 \approx 42\)
- \(6.98 \approx 7\)
- \(27.02 \approx 27\)
- \(33.01 \approx 33\)

### Step 2: Substitute the approximated values
Now, we substitute the approximated values into the equation:

\[ (42)^2 + (7)^2 - (27)^2 = (33)^2 - ? \]

### Step 3: Calculate the squares
Next, we calculate the squares of the rounded numbers:

- \(42^2 = 1764\)
- \(7^2 = 49\)
- \(27^2 = 729\)
- \(33^2 = 1089\)

### Step 4: Substitute the squared values
Now we substitute these squared values back into the equation:

\[ 1764 + 49 - 729 = 1089 - ? \]

### Step 5: Simplify the left side
Now we simplify the left side of the equation:

\[ 1764 + 49 = 1813 \]
\[ 1813 - 729 = 1084 \]

So, we have:

\[ 1084 = 1089 - ? \]

### Step 6: Solve for ?
Now we can solve for the question mark:

\[ ? = 1089 - 1084 \]
\[ ? = 5 \]

Thus, the approximate value that will come in place of the question mark (?) is **5**.

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