Question

Thực hiện phép tính:

1)\(\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{3\dfrac{1}{3}}\right)\)\(\left(\sqrt{1,2}+\sqrt{2}-4\sqrt{\dfrac{1}{5}}\right)\)

2) \(\left(\sqrt{12}+2\sqrt{27}\right)\dfrac{\sqrt{3}}{2}-\sqrt{150}\)

Answer 1

1: \(=\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{\dfrac{10}{3}}\right)\cdot\left(\sqrt{\dfrac{6}{5}}+\sqrt{2}-\dfrac{4}{\sqrt{5}}\right)\)

\(=\left(\dfrac{4\sqrt{3}}{3}+\dfrac{3\sqrt{2}}{3}+\dfrac{\sqrt{30}}{3}\right)\cdot\left(\dfrac{\sqrt{30}}{5}+\dfrac{5\sqrt{2}}{5}-\dfrac{4\sqrt{5}}{5}\right)\)

\(=\dfrac{\left(4\sqrt{3}+3\sqrt{2}+\sqrt{30}\right)\left(\sqrt{30}+5\sqrt{2}-4\sqrt{5}\right)}{15}\)

2: \(=\left(2\sqrt{3}+6\sqrt{3}\right)\cdot\dfrac{\sqrt{3}}{2}-5\sqrt{6}\)

\(=\dfrac{8\sqrt{9}}{2}-5\sqrt{6}=4\sqrt{9}-5\sqrt{6}=12-5\sqrt{6}\)