What approximate value should come in place of the question mark(?) in the following question (?)
(You are not expected to calculate the exact value )
`sqrt(624cdot9995)+(4cdot9989)^2=?div 1/(4cdot9900865)`

Options

A. 6
B. 50
C. 10
D. 125

Answer

To solve the problem, we need to evaluate the expression step by step. Let's break it down:

1. **Calculate the square root term:**
\[ \sqrt{624 \cdot 9995} \]
We can approximate \(9995\) as \(10000\) for easier calculation:
\[ \sqrt{624 \cdot 10000} = \sqrt{6240000} \]
Now, we can approximate \(6240000\):
\[ \sqrt{6240000} \approx \sqrt{6250000} = 2500 \]

2. **Calculate the squared term:**
\[ (4 \cdot 9989)^2 \]
Again, we can approximate \(9989\) as \(10000\):
\[ (4 \cdot 10000)^2 = (40000)^2 = 1600000000 \]

3. **Combine the two parts:**
Now, we add the results from step 1 and step 2:
\[ \sqrt{624 \cdot 9995} + (4 \cdot 9989)^2 \approx 2500 + 1600000000 \]
This sum is dominated by the squared term, so we can approximate it as:
\[ \approx 1600000000 \]

4. **Divide by the denominator:**
The expression we need to evaluate is:
\[ \frac{?}{\frac{1}{(4 \cdot 9900865)}} \]
We can simplify this as:
\[ ? \cdot (4 \cdot 9900865) \]
We can approximate \(9900865\) as \(10000000\):
\[ 4 \cdot 10000000 = 40000000 \]

5. **Setting up the equation:**
Now we have:
\[ 1600000000 = ? \cdot 40000000 \]
To find \(?\), we can rearrange the equation:
\[ ? = \frac{1600000000}{40000000} = 40 \]

Thus, the approximate value that should come in place of the question mark (?) is **40**.