(√7-√5)(√7+√5)

To simplify the expression \((\sqrt{7} - \sqrt{5})(\sqrt{7} + \sqrt{5})\), you can use the difference of squares formula, which states that \((a-b)(a+b) = a^2 - b^2\). Here, let: - \( a = \sqrt{7} \) - \( b = \sqrt{5} \) Now, apply the formula: \[ (\sqrt{7} - \sqrt{5})(\sqrt{7} + \sqrt{5}) = a^2 - b^2 \] Calculating \( a^2 \) and \( b^2 \): \[ a^2 = (\sqrt{7})^2 = 7 \] \[ b^2 = (\sqrt{5})^2 = 5 \] Now substitute these back into the expression: \[ a^2 - b^2 = 7 - 5 = 2 \] Thus, the simplified result is: \[ \boxed{2} \]