Question

( 5\(\sqrt{3}\) + 3\(\sqrt{5}\) ) : \(\sqrt{15}\)

Answer 1

\(=\dfrac{5\sqrt{3}+3\sqrt{5}}{\sqrt{15}}\\ =\dfrac{5\sqrt{3}}{\sqrt{15}}+\dfrac{3\sqrt{5}}{\sqrt{15}}\\ =\dfrac{5\sqrt{3}}{\sqrt{5}\sqrt{3}}+\dfrac{3\sqrt{5}}{\sqrt{3}\sqrt{5}}\\ =\sqrt{5}+\sqrt{3}\)

Answer 2

\(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}=\dfrac{5\sqrt{3}}{\sqrt{15}}+\dfrac{3\sqrt{5}}{\sqrt{15}}=\dfrac{\sqrt{25}\cdot\sqrt{3}}{\sqrt{5}\cdot\sqrt{3}}+\dfrac{\sqrt{9}\cdot\sqrt{5}}{\sqrt{5}\cdot\sqrt{3}}=\sqrt{\dfrac{25}{5}}+\sqrt{\dfrac{9}{3}}=\sqrt{5}+\sqrt{3}\)