The value of `(7sqrt2 +5) (7 sqrt2-5)` is

Options

A. 37
B. 171
C. 73
D. `14 sqrt2`

Answer

To solve the expression \((7\sqrt{2} + 5)(7\sqrt{2} - 5)\), we can use the difference of squares formula, which states that:

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

### Step-by-Step Solution:

1. **Identify \(a\) and \(b\)**:
- Here, let \(a = 7\sqrt{2}\) and \(b = 5\).

2. **Apply the difference of squares formula**:
- According to the formula, we have:
\[ (7\sqrt{2} + 5)(7\sqrt{2} - 5) = (7\sqrt{2})^2 - (5)^2 \]

3. **Calculate \(a^2\)**:
- Compute \((7\sqrt{2})^2\):
\[ (7\sqrt{2})^2 = 7^2 \cdot (\sqrt{2})^2 = 49 \cdot 2 = 98 \]

4. **Calculate \(b^2\)**:
- Compute \(5^2\):
\[ 5^2 = 25 \]

5. **Subtract \(b^2\) from \(a^2\)**:
- Now, substitute back into the formula:
\[ 98 - 25 = 73 \]

6. **Final Result**:
- Therefore, the value of \((7\sqrt{2} + 5)(7\sqrt{2} - 5)\) is:
\[ \boxed{73} \]