What approximate value will come in place of question mark (?) in the following questions. (You are not expected to find the exact value)
`sqrt(2024) xx sqrt(9.21) - 35.01 = ? xx 10.1`

Options

A. 10
B. 12
C. 14
D. 20

Answer

To solve the equation \( \sqrt{2024} \times \sqrt{9.21} - 35.01 = ? \times 10.1 \), we will follow these steps:

### Step 1: Approximate the square roots
First, we need to approximate the values of \( \sqrt{2024} \) and \( \sqrt{9.21} \).

- For \( \sqrt{2024} \), we can round it to the nearest perfect square. The closest perfect square is \( 2025 \), which is \( 45^2 \). Therefore, we approximate:
\[ \sqrt{2024} \approx \sqrt{2025} = 45 \]

- For \( \sqrt{9.21} \), we can approximate it to \( 9 \) (since \( 9.21 \) is very close to \( 9 \)). Thus:
\[ \sqrt{9.21} \approx 3 \]

### Step 2: Substitute the approximated values
Now we substitute these approximated values into the equation:
\[ \sqrt{2024} \times \sqrt{9.21} \approx 45 \times 3 \]

### Step 3: Calculate the product
Now we calculate the product:
\[ 45 \times 3 = 135 \]

### Step 4: Substitute into the equation
Now we substitute this back into the equation:
\[ 135 - 35.01 = ? \times 10.1 \]

### Step 5: Simplify the left side
Next, we simplify the left side:
\[ 135 - 35.01 \approx 135 - 35 = 100 \]

### Step 6: Set up the equation
Now we have:
\[ 100 = ? \times 10.1 \]

### Step 7: Solve for ?
To find the value of \( ? \), we divide both sides by \( 10.1 \):
\[ ? = \frac{100}{10.1} \approx 9.90 \]

### Step 8: Round to the nearest option
Since we are looking for an approximate value and the options are 10, 12, 14, and 20, we round \( 9.90 \) to the nearest whole number:
\[ ? \approx 10 \]

Thus, the approximate value that comes in place of question mark (?) is **10**.

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