Find the approximate value of (?) in the following questions.
12.012% of (231.989 + 417.91) + 90.98 = `(?)^(2)`

Options

A. 13
B. 15
C. 8
D. 10

Answer

To find the approximate value of (?) in the equation:

\[ 12.012\% \text{ of } (231.989 + 417.91) + 90.98 = (?)^2 \]

we will follow these steps:

### Step 1: Approximate the values
First, we will approximate the numbers involved in the equation.

- \( 231.989 \) can be approximated to \( 232 \)
- \( 417.91 \) can be approximated to \( 418 \)
- \( 90.98 \) can be approximated to \( 91 \)

So, we rewrite the equation using these approximations:

\[ 12.012\% \text{ of } (232 + 418) + 91 = (?)^2 \]

### Step 2: Calculate the sum inside the parentheses
Now, we calculate the sum:

\[ 232 + 418 = 650 \]

### Step 3: Calculate 12.012% of 650
Next, we need to find \( 12.012\% \) of \( 650 \).

To calculate \( 12.012\% \):

\[ 12.012\% = \frac{12.012}{100} = 0.12012 \]

Now, calculate:

\[ 0.12012 \times 650 \]

To simplify, we can approximate \( 0.12012 \) to \( 0.12 \):

\[ 0.12 \times 650 = 78 \]

### Step 4: Add 91 to the result
Now, we add \( 91 \) to the result from the previous step:

\[ 78 + 91 = 169 \]

### Step 5: Set up the equation
Now we have:

\[ 169 = (?)^2 \]

### Step 6: Solve for (?)
To find \( ? \), we take the square root of both sides:

\[ ? = \sqrt{169} = 13 \]

Thus, the approximate value of (?) is:

\[ \boxed{13} \]

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