Simplify each of the following expressions:
i) \((3 + \sqrt{3})(2 + \sqrt{2})\)
ii) \((3 + \sqrt{3})(3 - \sqrt{3})\)
iii) \( (\sqrt{5} + \sqrt{2})(\sqrt{5} + \sqrt{2})\)
iv)\((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})\)

i) \((3 + \sqrt{3})(2 + \sqrt{2})\)
\(\therefore \) \((3 + \sqrt{3})(2 + \sqrt{2}) \) \( = 6 + 3\sqrt{2} + 2\sqrt{3} + 6\)


ii) \((3 + \sqrt{3})(3 - \sqrt{3})\))
\(= 3^2 - (\sqrt{3})^2\)
Because, We know that,
(\(a + b)(a - b) = a^2 - b^2\)
\(\therefore (3 + \sqrt{3})(3 - \sqrt{3})\)
\( = 9 -3 = 6\)


iii)\((\sqrt{5} + \sqrt{2})^2\)
\(= (\sqrt{5})^2 + 2 × \sqrt{5}\sqrt{2} + (\sqrt{2})^2\)
Because, We know that, \((a + b)^2 = a^2 + 2 × a × b + b^2\)
\(= 5 + 2\sqrt{10} + 2\)
\(\therefore (\sqrt{5} + \sqrt{2})^2 = 7 + 2\sqrt{10}\)


iv) \((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})\)
\(= (\sqrt{5})^2 - (\sqrt{2})^2\)
Because, We know that, \((a + b)(a - b) = a^2 - b^2\)
\(\therefore\) \((\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2}) \)
\( = 5 -2 = 3\)