The value of `(sqrt5+sqrt2)(sqrt5-sqrt2)` is:

Options

A. 10
B. 7
C. 3
D. `sqrt3`

Answer

To solve the expression \((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})\), 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**:
In our case, we can identify:
- \(A = \sqrt{5}\)
- \(B = \sqrt{2}\)

2. **Apply the difference of squares formula**:
Using the formula, we substitute \(A\) and \(B\):
\[ (\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2}) = A^2 - B^2 \]

3. **Calculate \(A^2\) and \(B^2\)**:
- Calculate \(A^2\):
\[ A^2 = (\sqrt{5})^2 = 5 \]
- Calculate \(B^2\):
\[ B^2 = (\sqrt{2})^2 = 2 \]

4. **Subtract \(B^2\) from \(A^2\)**:
Now we substitute these values back into the formula:
\[ A^2 - B^2 = 5 - 2 \]

5. **Final Calculation**:
\[ 5 - 2 = 3 \]

Thus, the value of \((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})\) is **3**.