Question

* Thực hiện phép tính

c.\(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right).\dfrac{1}{2-\sqrt{5}}\)

d.\(\sqrt{\left(2-\sqrt{5}\right)^2}-\sqrt{5}\)

Answer 1

c) Ta có: \(\left(\dfrac{6-2\sqrt{2}}{3-\sqrt{2}}-\dfrac{5}{\sqrt{5}}\right)\cdot\dfrac{1}{2-\sqrt{5}}\)

\(=\left(\dfrac{2\left(3-\sqrt{2}\right)}{3-\sqrt{2}}-\sqrt{5}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}\right)\cdot\dfrac{1}{2-\sqrt{5}}\)

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

=1

d) Ta có: \(\sqrt{\left(2-\sqrt{5}\right)^2}-\sqrt{5}\)

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

=-2