The square root of `(272^(2) - 128^(2))` is :

Options

A. 256
B. 200
C. 240
D. 144

Answer

To solve the problem of finding the square root of \(272^2 - 128^2\), we can use the difference of squares formula. The difference of squares states that:

\[ a^2 - b^2 = (a + b)(a - b) \]

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
Here, we can let \(a = 272\) and \(b = 128\).

2. **Apply the difference of squares formula**:
Using the formula, we have:
\[ 272^2 - 128^2 = (272 + 128)(272 - 128) \]

3. **Calculate \(272 + 128\)**:
\[ 272 + 128 = 400 \]

4. **Calculate \(272 - 128\)**:
\[ 272 - 128 = 144 \]

5. **Substitute back into the equation**:
Now we substitute these values back into our equation:
\[ 272^2 - 128^2 = 400 \times 144 \]

6. **Find the square root**:
Now we need to find the square root of \(400 \times 144\):
\[ \sqrt{400 \times 144} = \sqrt{400} \times \sqrt{144} \]

7. **Calculate \(\sqrt{400}\) and \(\sqrt{144}\)**:
\[ \sqrt{400} = 20 \quad \text{and} \quad \sqrt{144} = 12 \]

8. **Multiply the results**:
Now we multiply these results:
\[ 20 \times 12 = 240 \]

Thus, the final answer is:
\[ \sqrt{272^2 - 128^2} = 240 \]