Which is greater between \(2 + \sqrt{7}\) and \(\sqrt{6} + \sqrt{5}\)?

Q.Which is greater between \(2 + \sqrt{7}\) and \(\sqrt{6} + \sqrt{5}\)?

\((2 + \sqrt{7})^2 = 4 + 7 + 4\sqrt{7} = 11 + \sqrt{112}\) \((\sqrt{6} + \sqrt{5})^2 = 6 + 5 + 2\sqrt{30} = 11 + \sqrt{120}\) Since \(\sqrt{120} > \sqrt{112}\), \(\therefore (\sqrt{6} + \sqrt{5})^2 > (2 + \sqrt{7})^2\) That means, \((\sqrt{6} + \sqrt{5}) > (2 + \sqrt{7})\) \(\therefore\) Between \((2 + \sqrt{7})\) and \((\sqrt{6} + \sqrt{5})\), \((\sqrt{6} + \sqrt{5})\) is greater.