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:

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

Here, we can identify:
- \(a = \sqrt{5}\)
- \(b = \sqrt{2}\)

Now, we can apply the formula:

1. **Calculate \(a^2\)**:
\[ a^2 = (\sqrt{5})^2 = 5 \]

2. **Calculate \(b^2\)**:
\[ b^2 = (\sqrt{2})^2 = 2 \]

3. **Subtract \(b^2\) from \(a^2\)**:
\[ a^2 - b^2 = 5 - 2 = 3 \]

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

\[ \boxed{3} \]