Question

(\(\sqrt{12}\) + \(\sqrt{75}\) + \(\sqrt{27}\)) : \(\sqrt{15}\)

Answer 1

\(=\dfrac{\sqrt{12}}{\sqrt{15}}+\dfrac{\sqrt{75}}{\sqrt{15}}+\dfrac{\sqrt{27}}{\sqrt{15}}\\ =\dfrac{\sqrt{4}}{\sqrt{5}}+\sqrt{5}+\dfrac{\sqrt{9}}{\sqrt{5}}\\ =\dfrac{\sqrt{20}}{5}+\sqrt{5}+\dfrac{\sqrt{45}}{5}\\ =\dfrac{2\sqrt{5}+3\sqrt{5}}{5}+\sqrt{5}=\dfrac{5\sqrt{5}}{5}+\sqrt{5}=\sqrt{5}+\sqrt{5}=2\sqrt{5}\)

Answer 2

\(\left(\sqrt{12}+\sqrt{75}+\sqrt{27}\right):\sqrt{15}=\sqrt{\dfrac{12}{15}}+\sqrt{\dfrac{75}{15}}+\sqrt{\dfrac{27}{15}}=\sqrt{\dfrac{4}{5}}+\sqrt{5}+\sqrt{\dfrac{9}{5}}=\dfrac{\sqrt{20}}{5}+\sqrt{5}+\dfrac{\sqrt{45}}{5}=\dfrac{5\sqrt{5}}{5}+\sqrt{5}=2\sqrt{5}\)