What approximate value should come in place of question mark(?) in the following questions?
`9.001^3=(?-3.3)xx89.867-:root(4)(624.99)`

Options

A. 53
B. 16
C. 28
D. 44

Answer

To solve the equation \( 9.001^3 = (? - 3.3) \times 89.867 \div \sqrt[4]{624.99} \), we will follow these steps:

### Step 1: Approximate \( 9.001 \)
Since \( 9.001 \) is very close to \( 9 \), we can approximate:
\[ 9.001 \approx 9 \]

### Step 2: Calculate \( 9^3 \)
Next, we calculate \( 9^3 \):
\[ 9^3 = 729 \]

### Step 3: Approximate \( 89.867 \)
We can round \( 89.867 \) to \( 90 \) for easier calculations:
\[ 89.867 \approx 90 \]

### Step 4: Calculate \( \sqrt[4]{624.99} \)
We can approximate \( 624.99 \) to \( 625 \) and find its fourth root:
\[ \sqrt[4]{625} = 5 \]

### Step 5: Substitute the approximations into the equation
Now we substitute the approximated values into the equation:
\[ 729 = (? - 3.3) \times 90 \div 5 \]

### Step 6: Simplify the equation
We can simplify the right side:
\[ 729 = (? - 3.3) \times 18 \]

### Step 7: Solve for \( ? - 3.3 \)
Now, we divide both sides by \( 18 \):
\[ ? - 3.3 = \frac{729}{18} \]
Calculating \( \frac{729}{18} \):
\[ \frac{729}{18} = 40.5 \]

### Step 8: Solve for \( ? \)
Now, we add \( 3.3 \) to both sides to find \( ? \):
\[ ? = 40.5 + 3.3 = 43.8 \]

### Step 9: Round to the nearest whole number
Since we are looking for an approximate value, we round \( 43.8 \) to \( 44 \).

### Final Answer
Thus, the approximate value that should come in place of the question mark (?) is:
\[ \boxed{44} \]

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