What approximate value will come in place of question mark (?) in the following questions ? (you are not expexted to calculate the exact value )
`38.98xx(195.98)^(1/2) div (41.87)=?^(1/2)-84.03xx7.06div(441.02)^(1/2)`

Options

A. 1520
B. 1590
C. 1680
D. 1630

Answer

To solve the given problem step by step, we will approximate the values and simplify the expression accordingly.

### Step 1: Approximate the Values
We will start by approximating the numbers in the expression:

- \( 38.98 \approx 39 \)
- \( 195.98 \approx 196 \)
- \( 41.87 \approx 42 \)
- \( 84.03 \approx 84 \)
- \( 7.06 \approx 7 \)
- \( 441.02 \approx 441 \)

### Step 2: Rewrite the Expression
Now, we can rewrite the expression using these approximations:

\[ \frac{39 \times (196)^{1/2}}{42} = ?^{1/2} - \frac{84 \times 7}{(441)^{1/2}} \]

### Step 3: Simplify the Square Roots
Next, we simplify the square roots:

- \( (196)^{1/2} = 14 \)
- \( (441)^{1/2} = 21 \)

Now, substituting these values back into the equation gives:

\[ \frac{39 \times 14}{42} = ?^{1/2} - \frac{84 \times 7}{21} \]

### Step 4: Calculate Each Side
Now, we calculate each side of the equation:

1. **Left Side:**
\[ \frac{39 \times 14}{42} = \frac{546}{42} = 13 \]

2. **Right Side:**
\[ \frac{84 \times 7}{21} = \frac{588}{21} = 28 \]

So the equation now looks like:

\[ 13 = ?^{1/2} - 28 \]

### Step 5: Solve for the Question Mark
Now, we can solve for \( ?^{1/2} \):

\[ ?^{1/2} = 13 + 28 = 41 \]

### Step 6: Square Both Sides
To find the value of \( ? \), we square both sides:

\[ ? = 41^2 = 1681 \]

### Conclusion
Thus, the approximate value that will come in place of the question mark (?) is:

\[ ? \approx 1681 \]