Which is greater between \((\sqrt{15} + \sqrt{3})\) and \((\sqrt{10} + \sqrt{8})\)?

Q.Which is greater between \((\sqrt{15} + \sqrt{3})\) and \((\sqrt{10} + \sqrt{8})\)?

\((\sqrt{15} + \sqrt{3})^2 = 15 + 3 + 2\sqrt{45} = 18 + 2\sqrt{45}\) \((\sqrt{10} + \sqrt{8})^2 = 10 + 8 + 2\sqrt{80} = 18 + 2\sqrt{80}\) Since \(\sqrt{80} > \sqrt{45}\), ∴ \((\sqrt{10} + \sqrt{8})^2 > (\sqrt{15} + \sqrt{3})^2\) That means, \((\sqrt{10} + \sqrt{8}) > (\sqrt{15} + \sqrt{3})\) ∴ Between \((\sqrt{15} + \sqrt{3})\) and \((\sqrt{10} + \sqrt{8})\), \((\sqrt{10} + \sqrt{8})\) is greater.