`1178.999xx25.0001- sqrt(?) xx 16.0011= 29075`

Options

A. 5
B. 15
C. 575
D. 625

Answer

To solve the equation \( 1178.999 \times 25.0001 - \sqrt{?} \times 16.0011 = 29075 \), we will approximate the numbers and find the value of the question mark step by step.

### Step 1: Approximate the Numbers
First, we will round the numbers to make calculations easier:
- \( 1178.999 \) can be approximated to \( 1179 \) (since it is closer to 1179).
- \( 25.0001 \) can be approximated to \( 25 \) (since it is very close to 25).
- \( 16.0011 \) can be approximated to \( 16 \) (since it is very close to 16).

So, we rewrite the equation as:
\[ 1179 \times 25 - \sqrt{?} \times 16 = 29075 \]

### Step 2: Calculate \( 1179 \times 25 \)
Now, we calculate \( 1179 \times 25 \):
\[ 1179 \times 25 = 29475 \]

### Step 3: Substitute Back into the Equation
Now substitute this back into the equation:
\[ 29475 - \sqrt{?} \times 16 = 29075 \]

### Step 4: Isolate the Square Root Term
Next, we isolate the square root term by moving it to the other side:
\[ 29475 - 29075 = \sqrt{?} \times 16 \]
\[ 400 = \sqrt{?} \times 16 \]

### Step 5: Solve for \( \sqrt{?} \)
Now, divide both sides by 16 to solve for \( \sqrt{?} \):
\[ \sqrt{?} = \frac{400}{16} = 25 \]

### Step 6: Square Both Sides
Finally, square both sides to find the value of the question mark:
\[ ? = 25^2 = 625 \]

Thus, the value of the question mark is:
\[ \boxed{625} \]

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