Question

Thực hiện tính \(\dfrac{2}{3}\sqrt{45}+\dfrac{\sqrt{42}}{\sqrt{21}}-20\sqrt{\dfrac{1}{5}}+\sqrt{10}.\sqrt{2}\)

Answer 1

\(=\dfrac{2}{3}\cdot3\sqrt{5}+\sqrt{2}-20\cdot\dfrac{1}{\sqrt{5}}+2\sqrt{5}\)

\(=2\sqrt{5}+\sqrt{2}-4\sqrt{5}+2\sqrt{5}=\sqrt{2}\)

Answer 2

\(\dfrac{2}{3}\sqrt{45}+\dfrac{\sqrt{42}}{\sqrt{21}}-20\sqrt{\dfrac{1}{5}}+\sqrt{10}.\sqrt{2}\)

\(=\dfrac{2}{3}\sqrt{3^2.5}+\sqrt{\dfrac{42}{21}}-4.\sqrt{25}.\sqrt{\dfrac{1}{5}}+\sqrt{10.2}\)

\(=\dfrac{2}{3}.3\sqrt{5}+\sqrt{2}-4.\sqrt{25.\dfrac{1}{5}}+\sqrt{2^2.5}\)

\(=2\sqrt{5}+\sqrt{2}-4.\sqrt{5}+2\sqrt{5}=\sqrt{2}\)