The approximate value of
`(7.230xx7.230-4.120xx4.120)/(7.230xx7.230+2xx7.230xx4.120+4.120xx4.120)`

Options

A. 3.24
B. 5
C. 0.274
D. 0

Answer

To solve the expression \((7.230 \times 7.230 - 4.120 \times 4.120) / (7.230 \times 7.230 + 2 \times 7.230 \times 4.120 + 4.120 \times 4.120)\), we can follow these steps:

### Step 1: Identify the Numerator and Denominator
The expression can be broken down into two parts:
- **Numerator**: \(7.230 \times 7.230 - 4.120 \times 4.120\)
- **Denominator**: \(7.230 \times 7.230 + 2 \times 7.230 \times 4.120 + 4.120 \times 4.120\)

### Step 2: Apply the Difference of Squares in the Numerator
The numerator resembles the difference of squares formula \(a^2 - b^2 = (a - b)(a + b)\). Here, we can set:
- \(a = 7.230\)
- \(b = 4.120\)

Thus, we can rewrite the numerator:
\[ 7.230 \times 7.230 - 4.120 \times 4.120 = (7.230 - 4.120)(7.230 + 4.120) \]

### Step 3: Calculate the Values
Calculate \(7.230 - 4.120\) and \(7.230 + 4.120\):
- \(7.230 - 4.120 = 3.110\)
- \(7.230 + 4.120 = 11.350\)

So, the numerator becomes:
\[ 3.110 \times 11.350 \]

### Step 4: Simplify the Denominator
The denominator can be recognized as a perfect square:
\[ 7.230 \times 7.230 + 2 \times 7.230 \times 4.120 + 4.120 \times 4.120 = (7.230 + 4.120)^2 \]
This is because it follows the form \(a^2 + 2ab + b^2 = (a + b)^2\).

### Step 5: Calculate the Denominator
Calculate \(7.230 + 4.120\):
- \(7.230 + 4.120 = 11.350\)

Thus, the denominator becomes:
\[ (11.350)^2 \]

### Step 6: Substitute Back into the Expression
Now we can substitute the values back into the expression:
\[ \frac{3.110 \times 11.350}{(11.350)^2} \]

### Step 7: Simplify the Expression
The \(11.350\) in the numerator and one \(11.350\) in the denominator will cancel out:
\[ \frac{3.110}{11.350} \]

### Step 8: Perform the Division
Now, we perform the division:
\[ 3.110 \div 11.350 \approx 0.274 \]

### Final Answer
Thus, the approximate value of the expression is:
\[ \boxed{0.274} \]