The square root of `73 ^(2) - 55 ^(2)` is :

Options

A. 42
B. 48
C. 18
D. 52

Answer

To solve the problem, we need to find the square root of \(73^2 - 55^2\). We can use the difference of squares formula, which states that \(a^2 - b^2 = (a - b)(a + b)\).

### Step-by-Step Solution:

1. **Identify the values**: Here, \(a = 73\) and \(b = 55\).

2. **Apply the difference of squares formula**:
\[ 73^2 - 55^2 = (73 - 55)(73 + 55) \]

3. **Calculate \(73 - 55\)**:
\[ 73 - 55 = 18 \]

4. **Calculate \(73 + 55\)**:
\[ 73 + 55 = 128 \]

5. **Substitute back into the formula**:
\[ 73^2 - 55^2 = 18 \times 128 \]

6. **Calculate \(18 \times 128\)**:
- Break it down:
\[ 18 \times 128 = 18 \times (100 + 28) = 18 \times 100 + 18 \times 28 \]
- Calculate each part:
\[ 18 \times 100 = 1800 \]
\[ 18 \times 28 = 504 \quad (\text{since } 18 \times 20 + 18 \times 8 = 360 + 144) \]
- Add them together:
\[ 1800 + 504 = 2304 \]

7. **Find the square root of \(2304\)**:
- We can check for perfect squares or use prime factorization.
- Alternatively, we can estimate:
- \(48 \times 48 = 2304\) (since \(48^2 = 2304\))

8. **Final Answer**:
\[ \sqrt{73^2 - 55^2} = \sqrt{2304} = 48 \]

### Final Answer:
The square root of \(73^2 - 55^2\) is \(48\).