What approximate value will come in place of question mark (?) in the given question? (You are not expected to calculate the exact value.)
`75.05%of(289.96+142.01)=(?)^2`

Options

A. 10
B. 16
C. 14
D. 18

Answer

To solve the equation \( 75.05\% \text{ of } (289.96 + 142.01) = (?)^2 \), we will approximate the values and simplify step by step.

### Step 1: Approximate the percentage
We can approximate \( 75.05\% \) to \( 75\% \) for easier calculations.

**Hint:** When dealing with percentages, rounding to the nearest whole number can simplify calculations.

### Step 2: Approximate the numbers
Next, we approximate \( 289.96 \) to \( 290 \) and \( 142.01 \) to \( 142 \).

**Hint:** Rounding numbers to the nearest ten or hundred can make arithmetic operations simpler.

### Step 3: Add the approximated values
Now, we calculate the sum:
\[ 290 + 142 = 432 \]

**Hint:** Always perform basic arithmetic operations carefully, even with approximated values.

### Step 4: Calculate \( 75\% \) of the sum
Now, we need to find \( 75\% \) of \( 432 \):
\[ 75\% = \frac{75}{100} = \frac{3}{4} \]
So,
\[ 75\% \text{ of } 432 = \frac{3}{4} \times 432 \]

**Hint:** Converting percentages to fractions can often simplify multiplication.

### Step 5: Simplify the multiplication
Calculating \( \frac{3}{4} \times 432 \):
\[ 432 \div 4 = 108 \]
Then,
\[ 3 \times 108 = 324 \]

**Hint:** Breaking down multiplication into smaller steps can help avoid mistakes.

### Step 6: Set the equation
Now we have:
\[ 324 = (?)^2 \]

**Hint:** This equation indicates that we need to find the square root of \( 324 \).

### Step 7: Calculate the square root
Taking the square root of both sides:
\[ ? = \sqrt{324} \]
We know that:
\[ \sqrt{324} = 18 \]

**Hint:** Familiarity with perfect squares can help you quickly find square roots.

### Final Answer
Thus, the approximate value that will come in place of the question mark (?) is:
\[ \boxed{18} \]