What approximate value should come in place of the question mark (?) in the following questions?
(Note: You are not expected to calculate the exact value.)
`33.99xxsqrt?+42.032xxsqrt?=(76)/(12.998)xx(?)`

Options

A. 81
B. 72
C. 169
D. 121

Answer

To solve the equation given in the question, we will follow these steps:

### Step 1: Write down the equation
The equation given is:
\[ 33.99 \times \sqrt{?} + 42.032 \times \sqrt{?} = \frac{76}{12.998} \times (?) \]

### Step 2: Approximate the constants
We can approximate the constants for easier calculations:
- \( 33.99 \approx 34 \)
- \( 42.032 \approx 42 \)
- \( 12.998 \approx 13 \)
- \( 76 \approx 78 \)

So, the equation simplifies to:
\[ 34 \times \sqrt{?} + 42 \times \sqrt{?} = \frac{78}{13} \times (?) \]

### Step 3: Combine like terms
On the left side, we can combine the terms:
\[ (34 + 42) \times \sqrt{?} = 76 \times \sqrt{?} \]
Thus, the equation becomes:
\[ 76 \times \sqrt{?} = \frac{78}{13} \times (?) \]

### Step 4: Simplify the right side
Now, we simplify the right side:
\[ \frac{78}{13} = 6 \]
So, the equation now looks like:
\[ 76 \times \sqrt{?} = 6 \times ? \]

### Step 5: Rearrange the equation
We can rearrange this equation:
\[ \frac{76 \times \sqrt{?}}{?} = 6 \]
This can be rewritten as:
\[ \frac{76}{\sqrt{?}} = 6 \]

### Step 6: Solve for \(\sqrt{?}\)
Now, we can solve for \(\sqrt{?}\):
\[ \sqrt{?} = \frac{76}{6} \]
Calculating this gives:
\[ \sqrt{?} \approx 12.67 \]

### Step 7: Square both sides to find ?
Now, squaring both sides gives:
\[ ? = (12.67)^2 \approx 160.68 \]

### Step 8: Round to the nearest whole number
Rounding \( 160.68 \) gives us approximately \( 169 \).

### Conclusion
Thus, the approximate value that should come in place of the question mark (?) is:
\[ ? \approx 169 \]