Question

\(\dfrac{\sqrt{10}-\sqrt{15}}{\sqrt{8}-\sqrt{12}}\)

\(\dfrac{\sqrt{6}-\sqrt{15}}{\sqrt{35}-\sqrt{14}}\)

\(\dfrac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}\)

Answer 1

\(\dfrac{\sqrt{10}-\sqrt{15}}{\sqrt{8}-\sqrt{12}}\)

\(=\dfrac{\sqrt{5}\left(\sqrt{2}-\sqrt{3}\right)}{\sqrt{4}\left(\sqrt{2}-\sqrt{3}\right)}\)

\(=\dfrac{\sqrt{5}}{\sqrt{4}}\)

\(=\dfrac{\sqrt{5}}{2}\)

Answer 2

\(\dfrac{\sqrt{6}-\sqrt{15}}{\sqrt{35}-\sqrt{14}}\)

\(=\dfrac{\sqrt{3}\left(\sqrt{2}-\sqrt{5}\right)}{\sqrt{7}\left(\sqrt{5}-\sqrt{2}\right)}\)

\(=-\dfrac{\sqrt{3}\left(\sqrt{5}-\sqrt{2}\right)}{\sqrt{7}\left(\sqrt{5}-\sqrt{2}\right)}\)

\(=-\dfrac{\sqrt{3}}{\sqrt{7}}\)

\(=-\dfrac{\sqrt{21}}{7}\)

____________

\(\dfrac{5+\sqrt{5}}{\sqrt{10}+\sqrt{2}}\)

\(=\dfrac{\sqrt{5}\left(\sqrt{5}+1\right)}{\sqrt{2}\left(\sqrt{5}+1\right)}\)

\(=\dfrac{\sqrt{5}}{\sqrt{2}}\)

\(=\dfrac{\sqrt{10}}{2}\)