On simplification of `((2.644)^(2)-(2.356)^(2))/(0.288)` We get:

Options

A. 1
B. 4
C. 5
D. 6

Answer

To simplify the expression \(\frac{(2.644)^2 - (2.356)^2}{0.288}\), we can follow these steps:

### Step 1: Recognize the Difference of Squares
The expression in the numerator, \((2.644)^2 - (2.356)^2\), is a difference of squares. We can use the identity:
\[ A^2 - B^2 = (A - B)(A + B) \]
where \(A = 2.644\) and \(B = 2.356\).

### Step 2: Apply the Difference of Squares Formula
Using the formula, we can rewrite the numerator:
\[ (2.644)^2 - (2.356)^2 = (2.644 - 2.356)(2.644 + 2.356) \]

### Step 3: Calculate \(A - B\) and \(A + B\)
Now we calculate \(2.644 - 2.356\) and \(2.644 + 2.356\):
- \(2.644 - 2.356 = 0.288\)
- \(2.644 + 2.356 = 5.000\)

### Step 4: Substitute Back into the Expression
Now we substitute these values back into the expression:
\[ \frac{(0.288)(5.000)}{0.288} \]

### Step 5: Simplify the Expression
Now we can simplify the expression:
\[ \frac{0.288 \times 5.000}{0.288} = 5.000 \]

### Final Answer
Thus, the simplified result of the expression is:
\[ \boxed{5} \]