Question

Find the product of $(\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{2}})$ and $(\sqrt{5}+\sqrt{2})$

Answer 1

$(\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{2}})\times (\sqrt{5}+\sqrt{2})$

$=\sqrt{\frac{3}{5}}\times \sqrt{5}+\sqrt{\frac{5}{2}}\times \sqrt{5}+\sqrt{\frac{3}{5}}\times \sqrt{2}+\sqrt{\frac{5}{2}}\times \sqrt{2}$

$=\sqrt{3}+\sqrt{5}+\sqrt{\frac{6}{5}}+\sqrt{\frac{25}{2}}$

$=\sqrt{3}+\sqrt{5}+\frac{\sqrt{30}}{5}+\frac{5\sqrt{2}}{2}$