`((10008.99)^(2))/(10009.001)xxsqrt(3589)xx0.4987=?`

Options

A. 3000
B. 300000
C. 3000000
D. 500

Explanation

To solve the equation \(\frac{(10008.99)^2}{10009.001} \times \sqrt{3589} \times 0.4987\) approximately, we will follow these steps:

### Step 1: Round off the numbers
- Round \(10008.99\) to \(10009\).
- Round \(10009.001\) to \(10009\).
- Round \(3589\) to \(3600\) (since \(3600\) is a perfect square).
- Round \(0.4987\) to \(0.50\).

### Step 2: Substitute the rounded values into the equation
Now we can rewrite the equation using the rounded values:
\[ \frac{(10009)^2}{10009} \times \sqrt{3600} \times 0.50 \]

### Step 3: Simplify the equation
- The \(10009\) in the numerator and denominator cancels out:
\[ 10009 \times \sqrt{3600} \times 0.50 \]

### Step 4: Calculate \(\sqrt{3600}\)
- \(\sqrt{3600} = 60\).

### Step 5: Substitute back into the equation
Now we have:
\[ 10009 \times 60 \times 0.50 \]

### Step 6: Calculate \(60 \times 0.50\)
- \(60 \times 0.50 = 30\).

### Step 7: Final multiplication
Now we multiply:
\[ 10009 \times 30 \]

### Step 8: Calculate \(10009 \times 30\)
- \(10009 \times 30 = 300270\).

### Conclusion
The approximate value of the expression is \(300270\).

### Step 9: Compare with options
Since we are looking for the closest approximation, we can round \(300270\) to \(300000\) or \(3 \text{ lakh}\).

### Final Answer
Thus, the required answer is approximately \(3 \text{ lakh}\).

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