Question

Tính

a) \(\sqrt{\dfrac{3}{30}}\) + \(\sqrt{\dfrac{1}{60}}\) - 2\(\sqrt{\dfrac{1}{15}}\)

b) ( \(5\sqrt{\dfrac{1}{5}}\) + \(\dfrac{1}{2}\sqrt{20}\) - \(\dfrac{5}{4}\sqrt{\dfrac{4}{5}+\sqrt{5}}\) ) : \(2\sqrt{5}\)

Answer 1

a: \(=\sqrt{\dfrac{1}{10}}+\sqrt{\dfrac{1}{60}}-\dfrac{2\sqrt{15}}{15}\)

\(=\dfrac{\sqrt{10}}{10}-\dfrac{2\sqrt{15}}{15}+\dfrac{\sqrt{15}}{30}\)

\(=\dfrac{3\sqrt{10}-3\sqrt{15}}{30}=\dfrac{\sqrt{10}-\sqrt{15}}{10}\)

b: \(=\dfrac{\left(\sqrt{5}+\dfrac{1}{2}\cdot2\sqrt{5}-\dfrac{5}{4}\cdot\dfrac{2}{\sqrt{5}}+\sqrt{5}\right)}{2\sqrt{5}}\)

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

\(=\dfrac{5}{2}:2=\dfrac{5}{4}\)