Question 114
The value of $$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$ is
Solution
$$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} - \frac{\sqrt{5}}{\sqrt{3}+\sqrt{2}})$$
=$$(\sqrt{5}+\sqrt{3})(\frac{3\sqrt{3}}{\sqrt{5}+\sqrt{2}} * \frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}- {\frac{\sqrt{5}}{\sqrt{3}+\sqrt{2} }x \frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}-\sqrt{2}}})$$
= $$(\sqrt{5}+\sqrt{3})(\sqrt{15} - \sqrt{6} - \sqrt{15} + \sqrt{10})$$ = $$(\sqrt{5}+\sqrt{3})(\sqrt{10}-\sqrt{6})$$ = $$2\sqrt{2}$$
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