Directions : What approximate value will come in place of the question mark (?) in the following questions? (You are not expected to calculate exact value).
`[(17.999)^2+(18.999)^2-(16.001)^2]divsqrt(9.01)=?xxsqrt(25.01)`

Options

A. 32
B. 22
C. 47
D. 29

Answer

To solve the given expression step by step, we will approximate the values and simplify the expression without calculating the exact values.

### Step 1: Approximate the values
We start with the expression:
\[ (17.999)^2 + (18.999)^2 - (16.001)^2 \]
We can approximate:
- \(17.999 \approx 18\)
- \(18.999 \approx 19\)
- \(16.001 \approx 16\)

So, we rewrite the expression as:
\[ (18)^2 + (19)^2 - (16)^2 \]

### Step 2: Calculate the squares
Now we calculate the squares:
- \( (18)^2 = 324 \)
- \( (19)^2 = 361 \)
- \( (16)^2 = 256 \)

Substituting these values back into the expression gives:
\[ 324 + 361 - 256 \]

### Step 3: Perform the addition and subtraction
Now, we perform the addition and subtraction:
\[ 324 + 361 = 685 \]
Then,
\[ 685 - 256 = 429 \]

### Step 4: Approximate the square root
Next, we need to divide this result by the square root of \(9.01\):
\[ \sqrt{9.01} \approx 3 \]

### Step 5: Set up the equation
Now we can set up the equation:
\[ \frac{429}{3} = ? \times \sqrt{25.01} \]
We approximate \(\sqrt{25.01} \approx 5\).

### Step 6: Substitute and solve for ?
Substituting the approximate value of \(\sqrt{25.01}\) gives:
\[ \frac{429}{3} = ? \times 5 \]

### Step 7: Solve for ?
To find ?, we rearrange the equation:
\[ ? = \frac{429}{3 \times 5} \]
Calculating the denominator:
\[ 3 \times 5 = 15 \]
Thus,
\[ ? = \frac{429}{15} \]

### Step 8: Perform the division
Now, we perform the division:
\[ 429 \div 15 \approx 28.6 \]

### Step 9: Round to the nearest whole number
Finally, rounding \(28.6\) gives us approximately:
\[ ? \approx 29 \]

### Conclusion
Thus, the approximate value that comes in place of the question mark (?) is:
\[ \boxed{29} \]