2. 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)$$(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})$$
###### Answer :

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, ($$a + b)(a - b) = a^2 - b^2$$
i.e., $$= 9 - 3$$
Therefore, $$(3 + \sqrt{3})(3 - \sqrt{3}) = 6$$

iii)$$= (\sqrt{5} + \sqrt{2})^2$$
$$= (\sqrt{5})^2 + 2 × \sqrt{5}\sqrt{2} + (\sqrt{2})^2$$
Because, We know that, $$(a + b)^2 = a^2 + 2 × a × b + b^2$$
i.e., $$= 5 + 2\sqrt{10} + 2$$
Therefore, $$(\sqrt{5} + \sqrt{2})(\sqrt{5} + \sqrt{2}) = 7 + 2\sqrt{10}$$

iv)= $$(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})$$
$$= (\sqrt{5})^2 - (\sqrt{2})^2$$
Because, We know that, $$(a + b)(a - b) = a^2 - b^2$$
i.e., $$= 5 - 2$$
Therefore, $$(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2}) = 3$$